# Light Reflection and Refraction Class 10 Science Exam Questions

Please refer to Light Reflection and Refraction Class 10 Science Exam Questions provided below. These questions and answers for Class 10 Science have been designed based on the past trend of questions and important topics in your class 10 Science books. You should go through all Class 10 Science Important Questions provided by our teachers which will help you to get more marks in upcoming exams.

## Class 10 Science Exam Questions Light Reflection and Refraction

Class 10 Science students should read and understand the important questions and answers provided below for Light Reflection and Refraction which will help them to understand all important and difficult topics.

Question: Write two different uses of concave mirrors.
Answer : The concave mirror is used as a shaving mirror and headlights of vehicles.

Question: What kind of image can be obtained on the screen ?

Question: What is the nature of the image formed by a concave mirror if the magnification produced by the mirror is + 2 ?

Question: What is relative refractive index ?
Answer : Refractive index of a medium with respect to another medium is called relative refractive index.

Question: Define the term angle of refraction.
Answer : The angle between the refracted ray and the normal at the point of incidence is called angle of refraction.

Question: Which metal is the best reflector of light ?
Answer : Silver metal is the best reflector of light.

Question: State two laws of reflection of light.
Answer : Two laws of reflection of light are :
(a) The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane.
(b) The angle of incidence is equal to the angle of reflection.

Question: What is absolute refractive index ?
Answer : Refractive index of a medium with respect to vacuum is called absolute refractive index.

Question: Between which two points of a concave mirror should an object be placed to obtain a magnification of – 2 ?
Answer : Between F and C.

Question: Define power of a lens.
Answer : The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it. It is also defined as the reciprocal of its focal length in metres.

Question: Define the term principal axis of a spherical mirror.
Answer : A straight line passing through the pole of spherical mirror and joining it to the centre of curvature of the mirror is known as the principal axis of the spherical mirror.

Question: Where is the image formed when an object is at large distance from a concave mirror ?
Answer : The image formed is at the focus of the mirror.

Question: Draw a ray diagram to show the formation of real image of an object when refraction of light takes place through a convex lens. Mark as per the new Cartesian sign convention the object-distance (u), image distance (v) and the focal length (f) and also write the relation between u, v and f.

Question: List four characteristics of the images formed by plane mirrors.
Answer : (a) Size of the image is equal to the size of object.
(b) Formed image is erect.
(c) Image formed by plane mirror is virtual.
(d) Formed image is laterally inverted.

Question: Define the term angle of incidence.
Answer : The angle between an incident ray and the normal at the point of incidence is called angle of incidence.

Question: Why is convex mirror used as a rear view mirror in vehicles ? State any one reason.
Answer : Convex mirror is used as a rear view mirror in vehicles because it gives a wider field view of the approaching traffic.

Question: The focal length of a lens is +25 cm. Write the power of this lens.

Question: State two laws of refraction of light.
Answer : Two laws of refraction of light are :
(a) The incident ray, the refracted ray and the normal to the interface of two transparent medium at the point of incidence, all lie in the same plane.
(b) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of medium.

Question: An object is placed 75 cm from a converging lens of focal length 25 cm. What is the nature of the image ?
Answer : The image is real, inverted and diminished as the object is placed beyond 2f.

Question: Redraw the following diagram on your answer-sheet and show the path of the reflected ray. Also mark the angle of incidence (∠i) and the angle of reflection (∠r) on the diagram.

Question: How should a ray of light be incident on a rectangular glass slab so that it comes out from the opposite side of the slab without being displaced?
Answer: A ray of light should be incident perpendicular to the surface of the rectangular glass slab so that it comes out from the opposite side of the slab without being displaced.

Question: Draw a ray diagram to determine the position of image formed of an object placed between the pole and the focus of a concave mirror.
Answer: Image formed by an object when it is kept between the pole and the focus of a concave mirror is

Question: The refractive index of diamond is 2.42. What is the meaning of this statement in relation to speed of light?
Answer: The refractive index of diamond is 2.42. This means the ratio of speed of light in vacuum to the speed of light in diamond is 2.42.

Question: Why does a ray of light bend when it travels from one medium into another?
Answer: A ray of light bends when it travels from one medium into another because of the change in speed of light from one medium to another.

Question: Draw the given diagram in your answer book and complete it for the path of ray of light beyond the lens.

An incident light coming parallel to the principal axis afer refraction through convex lens passes through focus.

Question: without suffering any deviationn beam of light from her laser torch by directing it from difierent directions on a convex lens held vertically. She was surprised to see that in a particular direction the beam of light continues to move along the same direction aftr passing through the lens. State the reason for this observation.
Answer: without suffering any deviationorch must incident the laser beam of light through optical centre of the convex lens. A ray of light though the optical centre of a lens passes without suffering any deviation.

Question. How can you identify the three types of mirrors without touching them?
a. If the image formed is erect, of same size, and at equal distance behind the mirror as object and is in front of the mirror, then mirror is plane.
b. If the image is of larger size and erect and changes to inverted and smaller size by changing the position of mirror from the object it is concave mirror.
c. If the image is smaller and erect for all positions of mirror from the object, it is a convex mirror.

Question. (a) What happens to a ray of fight when it travels from one medium to another having equal refractive indices?
(b) State the cause of refraction of fight.
(a) If a ray travels from one medium to another medium of same refractive indices then it will not bend and travels in a straight line.
(b) Change in speed of light is the cause of refraction. –

Question. A student focused the image of a candle flame on a white screen by placing the flame at various distances from a convex lens. He noted his observations:

a. From the above table, find the focal length of lens without using lens formula.
b. Which set of observations is incorrect and why?
c. In which case the size of object and image will be same? Give reason for your answer.
a. In observation (iii) of the table given u = 30 cm, v = 30 cm, which is only possible when u = v = 2f(at C) 2f = 30 or f=15 cm

Question. (a) Define power of a lens and write its SI unit.
(b) A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the lens, if image size is equal to the object size? Also, find the power of the lens.
a. Power of a lens is the ability of a lens to bend a ray of light incident upon it. It is equal to the  reciprocal of the focal length of the lens.

Question. Define the following terms in relation to concave spherical mirror:
a. Pole
b. Centre of curvature
d. Principal axis
e. Principal focus
f. Aperture
g. Focal length (each one mark)
a. The mid point of mirror is known as pole.
b. The centre of curvature of a spherical mirror is the centre of that sphere of which mirror is a part,
c. The distance between pole and centre of curvature is called radius of curvature of the mirror.
d. The straight line joining the pole and centre of curvature is called principal axis.
e. The point on the principal axis through which parallel rays to the principal axis passes or appear to pass after reflection.
f. The diameter of the mirror or size of the mirror is called aperture.
g. The distance between focus and pole of a mirror is the focal length of the mirror.

Question. What are the advantages and disadvantages of using a convex mirror for seeing traffic at the rear?
Advantage of Convex Mirror: It provide wider view of the rear traffic.
Disadvantage: It does not give the correct distance of the vehicle at the rear.

Question. What are the units of power of a lens?
If the focal length is measured in metre then the unit of power of a lens is dioptre.

Question. What is a prism?
A prism is an optical device with two triangular bases along with three rectangular lateral surfaces commonly inclined at an angle of 60°.

Question. Define the term reflection.
Answer : The bouncing back of a ray of light in the same medium after striking on a surface of an object.

Question. Define the terms:
a. Angle of incidence
b. Angle of reflection
c. Plane of incidence

a. The angle between incident ray and normal at the point of incidence is called angle of incidence +i .
b. The angle between the reflected ray and normal at
the point of incidence is called angle of reflection +r .
c. A plane containing, incident ray, normal, and reflected ray is known as plane of incidence.

Question. (a) What should be the position of the object, when a concave mirror is to be used:
(i) as a shaving mirror, and
(ii) in torches producing parallel beam of fight?
(b) A man standing in front of a mirror finds his image having a very small head and legs of normal size. What type of mirror are used in designing such a mirror?
(a) (i) Face must be placed in between the pole and focus of the mirror so that enlarged, erect image of face can be formed.
(ii) At focus, because rays coming from the focus after reflection will become parallel.
(b) It is a combination of convex mirror (small head) and plane mirror (legs of normal size).

Question. An object is placed at the focus of a convex lens. Draw a ray diagram to locate the position of the image formed, if any. State its position and nature.
Answer :  Image is formed at 3, image will be real, inverted and enlarged.

Question. Define the term magnification. Write its formula also.
Answer : Magnification m of a mirror gives the relative extent to which the size of image of an object is magnified w.r.t. size of object. It is the ratio of size of image (h2) to size
of an object (h1).

Question. State the laws of reflection.
a. The incident ray, the reflected ray and the normal
at the point of incidence are always in the same plane.
b. +i = +r

Question. Explain why we see the sign front of the some vehicles.
Answer : Because the image of laterally inverted written letter will once again laterally inverted in the rear view mirror of the vehicle going ahead and image so produced will be erect image of the word AMBULANCE.

Question. What is the radius of curvature of a plane mirror?
Answer : The radius of curvature of a plane mirror is infinite.

Question. How many images are formed by two parallel mirrors?
The images formed by two parallel plane mirrors will be infinite.

Question. Light enters from air to glass having refractive index 1.50. What is the speed of light in glass? Speed of light in air is 3#108 m/s.
Speed of light in glass

Question. The refractive index of diamond is 2.42. What is the meaning of this statement?
Answer : The meaning of refractive index of diamond is 2.42 is that speed of light in diamond is 1/2.42 times the speed of light in air/vacuum D,
i.e. speed of light in diamond

Question. If the image formed by a convex lens is of the same size as that of the object. What is the position and nature of the image with respect to the lens?
The image will be real, inverted and will be formed at centre of curvature of the lens.

Question. (a) Name the spherical mirror used as:
1. Shavingmirror,
2. Rearview mirror in vehicles,
3. Reflector in search – fights.
(b) Write any three differences between a real and
virtual image.
(a) 1. Concave mirror,
2. Convex mirror,
3. Concave parabolic
(b) Differences between a real and virtual image :

Question. With the help of ray diagrams differentiate between a converging lens and a diverging lens.

Question. If the image formed by a spherical mirror for all positions of the object placed in front of it, is always erected and diminished, what type of mirror is it?
Answer : It is a convex mirror. Ray diagram for any position  of object

Question. Name the type of lens that can be used . as magnifying glass. Give reason(s) and draw a ray diagram to support your answer.
A convex lens of smaller focal length can be used as magnifying glass. When an object is placed in between the pole and focus of the convex lens then enlarged, erected and same side of object image is formed.

Question. Write down four important characteristics of image formed by a plane mirror.
Image is virtual, erect, laterally inverted and of same size as object.

Question. An object is placed at the following distances from a concave mirror of focal length 15 cm.
(a) 10 cm
(b) 20 cm
(c) 30 cm
(d) 40 cm
Which position of the object will produce:
(i) Virtual image
(ii) A diminished real image
(iii) An enlarged real image
(iv) An image of same size.
Answer :  Given, concave mirror of f= 15 cm.
a. When object is placed at a distance 10 cm from mirror (between P and f) image is virtual, enlarged and erected.
b. For object in between 2F and 3 i.e. 40 cm image is inverted, diminished and real.
c. For object in between F and C (20 cm), image is inverted, enlarged and real beyond 2F(C).
d. For object at 2F (30 cm), the image is of same size.

Question. Give two uses of a convex lens.
Convex lens are used in (i) spectacles, (ii) telescopes,
(iii) microscopes, (iv) camera.

Question. Give one use of a concave lens.
Concave lenses are used in (i) shaving mirror, (ii) flash lights,

Question. (a) What is meant by refraction of fight?
(b) If on applying Cartesian sign convention for spherical lenses, the image distance obtained is negative, state the significance of the negative sign.
(a) When a ray of light passes from one medium to another it bends from its path. The phenomenon of bending a ray of light when it passes from one medium to another is called refraction of light.
(b) In a lens if the image distance is negative then its meaning is that image formed is at the same side of object, virtual and erect. The lens is concave lens.

Question. What is minimum number of rays required for locating the image formed by a concave mirror for an object?
Draw a ray diagram to show the formation of a virtual image by a concave mirror.
Answer : We require minimum two rays for locating the image formed by a concave

Question. The absolute refractive index of Ruby is 1·7. Find the speed of light in Ruby. The speed of light in vacuum is 3 × 108 m/s.
We know that,
Refractive index of Ruby (μ)

Question. The power of a lens in +5 diopters. What is the nature and focal length of this lens ? At what distance from this lens should an object be placed so as to get its inverted image of the same size ?
Answer : Given, P = + 5D
We have,

Focal length, f = 20 cm (or + 20 cm).
Since, focal length of the lens is positive. Therefore, the nature of lens is convex. Same size and inverted image is formed when
Magnification, m = – 1

Question. A student holding a mirror in his hand, directed the reflecting surface of the mirror towards the Sun. He then directed the reflected light on to a sheet of paper held close to the mirror.
(a) What should he do to burn the paper ?
(b) Which type of mirror does he have ?
(c) Will he be able to determine the approximate value of focal length of this mirror from this activity ? Give reason and draw ray diagram to justify your answer in this case.
Answer : (a) He should place the sheet of paper at the focus of the mirror to burn the paper.
(b) He has a concave mirror.
(c) Yes, the sheet of paper will start burning at the focus of the mirror which will give approximate value of focal length, i.e., the distance between mirror and the focal point where the sheet of paper starts burning.

A concave mirror forms a real image of the sun.

Question. The diagram given below shows an object O and its image I.

Without actually drawing the ray diagram, state the following :
(i) Type of lens (Converging/Diverging)
(ii) Name two optical instruments where such an image is obtained.
(iii) List three characteristics of the image formed if this lens is replaced by a concave mirror of focal length ‘f’ and an object is placed at a distance ‘f/2’ in front of the mirror.
(i) Converging.
(ii) (1) Simple Microscope.
(2) Magnifying Glass
(iii) The image formed will be behind the mirror, enlarged, virtual and erect.

Question. A 10 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 12cm.
The distance of the object from the lens is 18 cm. Find the nature, position and size of the image formed.
Answer : Given : Height of object, h1 = + 10 cm.
Focal length, f = + 12 cm.
Object distance, u = – 18 cm.
From the lens fomula,

The position of image formed is at distance of 36 cm from the convex lens.
Since the value of magnification is more than 1 (it is 2), the image formed is larger than object.
The minus sign of magnification shows that image is formed below the principal axis. Hence, the image formed is real and inverted.

Question. List four precautions which a student should observe while determining the focal length of a given convex lens by obtaining image of a distant object on a screen.
Answer : Precantions as follows :
(a) Fix the lens vertically in lens holder.
(b) Base of lens and white screen should be in a line with measuring scale.
(c) There should not be any obstacle in path of lens.
(d) Record the position of lens and screen when sharp image is formed.

Question. An object of height 4.0 cm is placed at a distance of 30 cm from optical centre ‘O’ of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’ and principal focus ‘F’ on the diagram. Also find the approximate ratio of size of image to the size of object.
Answer : Given, f = + 20 cm, u = – 30 cm, ho = 4 cm
We know that,

Thus, the height or size of the image is 8 cm. The minus sign shows that this height is in the downward direction, that is, the image is formed below the axis.

Question. A student focuses the image of a candle flame, placed at about 2 m from a convex lens of focal length 10 cm, on a screen. After that he moves gradually the flame towards the lens and each time focuses its image on the screen.
(a) In which direction does he move the lens to focus the flame on the screen ?
(b) What happens to the size of the image of the flame formed on the screen ?
(c) What difference is seen in the intensity (brightness) of the image of the flame on the screen ?
(d) What is seen on the screen when the flame is very close (at about 5 cm) to the lens ?
Answer : (a) He moves the lens away from the screen to focus the image.
(b) Size of the image increases.
(c) The intensity of image decreases as the flame moves towards the lens.
(d) Nothing can be seen as the image formed is virtual.

Question. An object is placed at a distance of 30 cm from a concave lens of focal length 15 cm. List four characteristics (nature, position, etc.) of the image formed by the lens.
Answer : Given : u = – 30 cm, f = – 15 cm. (for concave lens)
We know that,

Characteristics of image :
(a) The image is formed at a distance of 10 cm from the concave lens on the left side.
(b) Image formed is virtual.
(c) Image formed is erect.
(d) The size of the image formed is diminished.

Question. If the image formed by a lens for all positions of an object placed in front of it is always erect and diminished, what is the nature of this lens ? Draw a ray diagram to justify your answer. If the numerical value of the power of this lens is 10 D, what is its focal length in the Cartesian system ?
Answer : It is a concave lens (diverging lens).

Question. An object is placed at a distance of 30 cm in front of a convex mirror of focal length 15 cm. Write four characteristics of the image formed by the mirror.
Answer : Given : u = – 30 cm, f = 15 cm.

Characteristics of image :
(a) Image formed is erect.
(b) Image formed is small in size.
(c) Image formed is virtual.
(d) Image is formed at a distance of 10 cm behind the mirror between focus and pole.

Question. Draw ray diagrams to show the formation of three times magnified (a) real and (b) virtual image of an object by a converging lens. Mark the positions of O, F and 2F in each diagram.
Answer : (a) For real image : To get three times magnified image, the object is placed between F1 and 2F1.

(b) For virtual image : To get three times magnified image, the object is placed between the F1 and optical centre O.

Question. A 3 cm tall object is placed 18 cm in front of a concave mirror of focal length 12 cm. At what distance from the mirror should a screen be placed to see a sharp image of the object on the screen. Also calculate the height of the image formed.
Answer : Using mirror equation :
u = – 18 cm, f = – 12 cm, v = ?, h1 = + 3 cm, h2 = ?

Thus, to obtain a sharp image of the object, the screen should be placed at a distance of 36 cm, in front of the mirror.

Question. An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what  distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.
Answer : Given : u = – 15 cm, f = – 10 cm, ho = 4 cm
Using the mirror formula

Thus, to obtain a sharp image of the object, the screen should be placed in front of the mirror at a distance of 30 cm.

Question. Define the following terms related to spherical mirrors :
(a) Centre of curvature, (b) Pole and (c) Aperture.
Answer : (a) The centre of curvature of a spherical mirror is the centre of the sphere of which the mirror is a part.
(b) The pole of a spherical mirror is the geometric centre of the spherical surface of the mirror.
(c) The plane surface area of the mirror through which the light rays enter and fall on the mirror is called its aperture.

Question. (a) What is an optical medium ?
(b) What do you mean by :
(i) an optically dense medium ?
(ii) an optically rare medium ?
Answer : (a) A medium through which light can travel is called an optical medium.
(b) (i) While passing from one medium to the other, if the speed of light slows down, then the second medium is said to be optically denser than the first medium.
(ii) While passing from one medium to the other, if the speed of light increases, then the second medium is said to optically rarer than the first medium.

Question. (a) State the two laws of reflection of light.
(b) A light ray is incident normally on a plane mirror. What is its angle of incidence ?
Answer : (a) The two laws of reflection are :
(i) The incident ray, the reflected ray and the normal at the point of incidence, lie in the same plane.
(ii) The angle of incidence is equal to the angle of reflection (∠i = ∠r).
(b) The angle of incidence will be 0°.

Question. (a) Define lateral shift.
(b) State and explain the factors on which it depends.
Answer : (a) The perpendicular distance between the path of emergent ray and the direction of incident ray is called lateral shift.
(b) Lateral shift depends on the following factors :
(i) It is directly proportional to the thickness of glass slab.
(ii) It is directly proportional to the angle of incidence.
(iii) It is directly proportional to the refractive index of the glass slab.
(iv) It is inversely proportional to the wavelength of the light used.

Question. (a) What is meant by magnification ? Write its expression.
(b) What is its sign for (i) real, (ii) virtual image ?
Answer : (a) The ratio of height of the image to the height of the object is called linear magnification. If the height of the image is ‘I’ and that of the object is ‘O’, then the magnification ‘m’ is :

(b) (i) For a real image, magnification is negative.
(ii) For a virtual image, magnification is positive.

Question. Write the relationship between the S.I. unit of the power of a lens and S.I. unit of focal length.
Answer : Reciprocal of focal length of a lens, expressed in metre, is called the power of that lens. Its S.I. unit is 1 dioptre
(1 D), where 1 D = 1 m–1.

Question. Draw the following diagrams in your answer book and show the formation of the image of object AB by completing the ray diagrams

Question. (a) The figure shows the position of an object AB in relation to a converging lens whose foci are Fand F2. Draw two rays to locate the position of image.

(b) State three characteristics of image formed.

(b) The three characteristics of the image formed are :
(i) Virtual and erect, (ii) magnified and (iii) behind the object.

Question. An object is kept 40 cm in front of a concave mirror of focal length 20 cm. Find the position and nature of the image. Draw a ray diagram to show the formation of image in this case.
Answer : Given : u = – 40 cm
f = – 20 cm
Using mirror formula,

Hence, image will be formed at a distance of 40 cm and it will be real and inverted.
Ray Diagram

Question. Draw a labelled ray diagram for the formation of image by a convex lens of focal length 15 cm when the object is placed at a distance of 25 cm from the lens.
Determine the size of the image formed, if size of the object is 4 cm.
Answer : Given : u = – 25 cm
f = 15 cm
Using lens formula

Question. We wish to obtain an equal sized inverted image of a candle flame on a screen kept at distance of 4 m from the candle flame.
(a) Name the type of lens that should be used.
(b) What should be the focal length of the lens and at what distance from the candle flame the lens be placed ?
(c) Draw a labelled diagram to show the image formation in this case.
A 5 cm tall object is placed at a distance of 30 cm from a convex mirror of focal length 15 cm. Find the position, size and nature of the image formed.

(b) For real image in convex lens object is placed at 2f.

Hence, virtual image is formed by the convex mirror and the size of image is smaller than size of object.

Question. While tracing the path of a ray of light passing through a rectangular glass slab a student tabulated his observations. If in his experiment for two readings he takes two values of ∠i as 40° and 50°, what should be the correct values of ∠e and ∠r in each case ?
We know that for light the angle of incidence (∠i) should be equal to angle of emergence (∠e)
If ∠i = 40° then ∠e = 40°
∠i = 50° then ∠e = 50°
For the glass refractive index is 1.5, hence

Question. State Snell’s law of refraction of light. Express it mathematically. Write the relationship between absolute refractive index of a medium and speed of light in vacuum.
The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media

Relation between absolute refractive index of a medium and speed of light in vacuum.

Question. An object of height 2.0 cm is placed on the principal axis of a convex lens of focal length 10 cm. The distance of the object from the optical centre (O) of the lens is 20 cm. Choose a proper scale and draw a ray diagram to find the position, nature and size of the image. Also measure and write the size of the image and its distance from the optical centre of the lens.

Answer : Given : hi = 2 cm
u = – 20 cm
f = + 10 cm
Using lens formula,

Question. An object is placed perpendicular to the principal axis of a convex lens of focal length 8 cm. The distance of the object from the lens is 12 cm. Find the position and nature of the image.
Answer : Given : f = + 8 cm
u = – 12 cm
v = ?
Using lens formula,

So, image is formed behind the lens is real, inverted and magnified.

Question. Draw each of the following diagrams on your answer sheet and show the path of the ray after reflection in each case.

Question. An object is placed perpendicular to the principal axis of a convex lens of focal length 14 cm. The distance of the object from the lens is 21 cm. Find the position and nature of the image formed.
Answer : Given : f = + 14 cm
u = – 21 cm
v = ?
Using lens formula,

So, the image formed is real, inverted and formed behind the lens.

Question. Define the term magnification as referred to spherical mirrors. If a concave mirror forms a real image 40 cm from the mirror, when the object is placed at a distance of 20 cm from its pole, find the focal length of the mirror.
Answer : The relative extent to which the image of an object is magnified with respect to object size is known as magnification.

Question. The magnification of an image formed by a lens is –1.
If the distance of the image from the optical centre of the lens is 25 cm, where is the object placed ? Find the nature and focal length of the lens. If the object is displaced 15 cm towards the optical centre of the lens, where would the image be formed ? Draw a ray diagram to justify your answer.
m = – 1 i.e., Image is real, inverted and same size as the object and,
Object distance = Image distance = 2f = 35 cm
Nature of lens: convex or converging
As 2f = 35 cm

On displacing the object 20 cm towards the lens, the object distance becomes 15 cm (35 cm – 20 cm) i.e., it lies between F and O of the lens.
Image formed now is virtual and on the same side of lens as the object.

Question. To find the image distance for varying object distances in case of a convex lens of focal length 15 cm, a student obtains on a screen a sharp image of a bright object by placing it at 20 cm distance from the lens. After that he gradually moves the object away from the lens and each time focuses the image on the screen.
(a) In which direction-towards or away from the lens does he move the screen to focus the object ?
(b) How does the size of image change ?
(c) Approximately at what distance does he obtain the image of magnification –1 ?
(d) How does the intensity of image change as the object moves farther and farther away from the lens ?
Answer : (a) He should move the screen towards the lens.
(b) Size of the image decreases gradually.
(c) Nearly 30 cm from the lens.
(d) Intensity of the image gradually increases.

Question. If the image formed by a lens for all positions of the object placed in front of it is always virtual, erect and diminished, state the type of the lens. Draw a ray diagram in support of your answer. If the numerical value of focal length of such a lens is 20 cm, find its power in new cartesian sign conventions.
Answer : Lens should be concave.

Focal length = −20 cm ( lens is concave, hence f is –ve)
Power = P = 1/f = 100/ −20cm = −5 D

Question. The linear magnification produced by a spherical mirror is +3. Analyse this value and state the (i) type of mirror and (ii) position of the object with respect to the pole of the mirror. Draw ray diagram to show the formation of image in this case.
(b) Between the pole and focus

Question. List two properties of the images formed by convex mirrors. Draw ray diagram in support of your answer.
Answer : Image formed by the convex mirrors are virtual and smaller than the real object.

Question: A ray of light is incident on a convex mirror as shown. Redraw the diagram and complete the path of this ray aftr reflection from the mirror. Mark angle of incidence and angle of reflection on it.

Question: AB and CD, two spherical mirrors, from parts of a hollow spherical ball with its centre at O as shown in the diagram. If arc AB = 1 2 arc CD, what is the ratio of their focal lengths? State which of the two mirrors will always form virtual image of an object placed in front of it and why?

Answer: Focal length of a mirror is given by Focal length =Radius of curvature/2 Since both the mirrors have same radius of curvature, therefore focal length of the two mirrors will be same, i.e.,f1/f2=1/1 Since virtual image is always formed by convex mirror. The mirror AB will always form virtual image.

Question:  List four specific characteristics of the images of the objects formed by convex mirrors.
Answer: Characteristics of image formed by convex mirrors :
• Diminished
• Virtual and erect
• The image formed is closer to the mirror than the object placed
• Image is formed behind the mirror.

Question: The linear magnification produced by a spherical mirror is +3. Analyse this value and state the (i) type of mirror and (ii) position of the object with respect to the pole of the mirror. Draw a ray diagram to show the formation of image in this case.
Answer: Positive value of the magnification indicates that image is virtual and erect.
(i) Since the image is magnified, the mirror is concave.
(ii)The object is between pole and focus of the mirror as shown

Question: The linear magnification produced by a spherical mirror is –1. Analysing this value state the (i) type of mirror and (ii) position
of the object with respect to the pole of the mirror. Draw any diagram to justify your answer.
Answer: (i) Concave mirror because the image is real,inverted.
(ii) Object is placed at C.

Question: Draw a ray diagram to show the path of the reflected ray corresponding to an incident ray which is directed towards the principal focus of a convex mirror. Mark on it the angle of incidence and the angle of refiection.

Question: Draw a ray diagram to show the path of the reflected ray corresponding to an incident ray of light parallel to the principal axis of a concave mirror. Mark the angle of incidence and angle of reflection on it.

Question: List two possible ways in which a concave mirror can produce a magnified image of an object placed in front of it. State the difierence if any between these two images.
Answer: A concave mirror can produce a magnified image of an object when object is placed :
(1) In between its pole and its focus,
(2) In between its focus and its centre of curvature.
Difference between these two images :
The image produced in first case will be virtual and erect.
The image produced in second case will be real and inverted.

Question:  Draw a ray diagram to show the path of the reflected ray corresponding to an incident ray which is directed parallel to the principal axis of a convex mirror, Mark on it the angle of incidence and the angle of refiection.

Question: The linear magnification produced by a spherical mirror is –1/5. Analysing this value state the (i) type of spherical mirror and
(ii) the position of the object with respect to the pole of the mirror. Draw ray diagram to justify your answer.
(ii) Object is placed beyond C.

Question: To construct ray diagram we use two light rays which are so chosen that it is easy to know their directions aftr reflection from the mirror. List these two rays and state the path of these rays aftr refiection. Use these rays to locate the image of an object placed between centre of curvature and focus of a concave mirror.
Answer: A ray parallel to the principal axis, after rflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror.
A ray passing through the centre of a curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path. The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.

Question: If the image formed by a lens for all positions of the object placed in front of it is always virtual, erect and diminished, state the type of the lens. Draw a ray diagram in support of your answer. If the numerical value of focal length of such a lens is 20 cm, find its power in new cartesian sign conventions.
Answer: Concave lens always forms virtual, erect and diminished image for all positions of the object.

Question: The image of a candle flame placed at a distance of 40 cm from a spherical lens is formed on a screen placed on the other side of the lens at a distance of 40 cm from the lens. Identify the type of lens and write its focal length. What will be the nature of the image formed if the candle flame is shifed 25 cm towards the lens? Draw a ray diagram to justify your answer.
Answer: Given : u = –40 cm, v = 40 cm
1/f =1/4+1/40=2/40 ⇒ f =20 cm
Type of lens : Convex lens
Focal length = 20 cm
Nature of the image will be virtual and erect if the candle flame is shifted 25 cm towards the lens.

Question: If the image formed by a lens for all positions of the object placed in front of it is always virtual, erect and diminished, state the type of the lens. Draw a ray diagram in support of your answer. If the numerical value of focal length of such a lens is 20 cm, find its power in new cartesian sign conventions.
Answer: Concave lens always forms virtual, erect and diminished image for all positions of the object.

Question: An object of height 6 cm is placed perpendicular to the principal axis of a concave lens of focal length 5 cm. Use lens formula to determine the position, size and nature of the image if the distance of the object from the lens is 10 cm.

Question: What is the principle of reversibility of light? Show that the incident of light is parallel to the emergent ray of light when light falls obliquely on a side of a rectangular glass slab.
Answer: Principle of reversibility of light states that the light will follow exactly the same path if the direction is
eversed. Using Snell’s law of refraction,

Question: What is understood by lateral displacement of light? Illustrate it with the help of a diagram. List any two factors on which the lateral displacement in a particular substance depends.
Answer: When a ray of light is incident obliquely on a parallel sided glass slab, the emergent ray shifts laterally. the perpendicular distance between the direction of the incident ray and emergent ray is called lateral shifts. The factors on which the lateral displacement depends are:
(i) thickness of the refracting material.
(ii) the refractive index of the material.

Question: At what distance should an object be placed from a convex lens of focal length 18 cm to obtain an image at 24 cm from it on the other side. What will be the magnification produced in this case?
Answer: Focal length of convex lens, f = +18 cm Image distance from the lens, v = +24 cm By using lens formula,

Question: The image of an object placed at 60 cm in front of a lens is obtained on a screen at a distance of 120 cm from it. Find the focal length of the lens. What would be the height of the image if the object is 5 cm high?

Question: For which position of the object does a convex lens form a virtual and erect image? Explain with the help of a ray diagram.
Answer: When an object is placed between F1 and optical centre, O of a convex lens, it forms a virtual and erect image. The ray diagram for this situation can be drawn as follows :

Question. A ray of light is incident obliquely on a glass slab. Draw a ray diagram showing the path of the light ray.
Clearly, mark angle of incidence, angle of refraction, angle of emergence and lateral displacement of the ray.
Give a formula to find refractive index of glass slab in terms of angle of incidence and angle of refraction.
Answer : When a ray passes from optical rarer to denser medium, it bends towards the normal and vice versa.

Question. (a) For the same angle of incidence 45°, the angle of refraction in two transparent media; I and II is 20° and 30° respectively. Out of I and II, which medium is optically denser and why?
(b) Light enters from air to diamond which has refractive index of 2.42. Calculate the speed of light in diamond, if speed of light in air is 3#108 ms-1.
a. For the same angle of incidence. The refracted ray in medium I deviates less than in medium II.
Hence medium I is more denser than medium II.

b. Refractive index of diamond = 2.42
Speed of light in air = 3#108 m/s
Speed of light in diamond = ?

Question. (a) A ray of light falls normally on a face of a glass slab. What are the values of angle of incidence and angle of refraction of this ray?
(b) Light enters from air to a medium X. Its speed in medium X becomes 1.5#108 ms-1. Find the refractive index of medium X.
a. When a ray of light falls normally on a glass slab then i = 0, and r = 0
b. vm 1.5 x 10 m/s
= # 8
c = 3×108 m/s
We know Refractive index

Question. (a) Water has refractive index 1.33 and alcohol has refractive index 1.36. Which of the two medium is optically denser? Give reason for your answer.
Draw a ray diagram to show the path of a ray of light passing obliquely from water to alcohol.
(b) The absolute refractive index of diamond is 2.42 and the absolute refractive index of glass is 1.50.
Find the refractive index of diamond with respect to glass.
a. More refractive index means more optical denser medium. Here refractive index of water is 1.33 and of alcohol is 1.36 nAl > nw .
Hence alcohol is more optical denser than water

Question. A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of image and magnification. Describe what happens to the image as the needle is moved farther from the mirror.
Answer : Given: u =- 12 cm
f =+ 15 cm
h1 = 4.5 cm
v = ?, m = ?
Mirror formula,

Size of image is smaller than size of object.

Question. (a) State Snell’s law of refraction.
(b) When a ray of light travelling in air enters obliquely into a glass slab, it is observed that the light ray emerges parallel to the incident ray but it is shifted sideways slightly. Draw a ray diagram to illustrate it.
(a) Snell’s law = sin i/sin r  = constant
(b)

Question. A student wants to project the image of a candle flame
on a screen 60 cm in front of a mirror by keeping the flame at a distance of 15 cm from its pole.
a. Write the type of mirror he should use.
b. Find the linear magnification of the image produced.
c. What is the distance between the object and its image?
d. Draw a ray diagram to show the image formation in this case.
Given: v =- 60 cm
u =- 15 cm
a. Since the image is real the minor is concave

Question. Discuss the position and nature of the image formed by a concave mirror when the object is moved from infinity towards the pole of the mirror.
Answer : When an object is moved from ∞ toward the pole of a concave mirror then its image moves from focus to infinity.

Question. State the laws of refraction.
Answer : Snell’s laws of refraction
a. Incident ray, refracted ray and normal to the point of incidence lie in the same plane.
b.  sin i/sin r = 1/2n

Question. (a) A security mirror used in a big showroom has radius of curvature 5 m. If a customer is standing at a distance of 20 m from the cash counter, find the position, nature and size of the image formed in the security mirror.
(b) Neha visited a dentist in his clinic. She observed that the dentist was holding an instrument fitted with a mirror. State the nature of this mirror and reason for its use in the instrument used by dentist.
(a) We know that convex mirror is used in security mirrors and a customer is standing at a distance of 20 m (object distance ) and radius of curvature of mirror is 5 m
Given,
Radius of curvature, R = + 5 m
Object distance, u = – 20 m
Image distance, v = ?
Height of image, h’ = ?

The image is virtual, erect of smaller in size by a factor of 0.11.
(b) Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light. The dentists use concave mirrors to see large images of the teeth of patients.

Question. Rishi went to a palmist to show his palm. The palmist used a special lens for this purpose.
(i) State the nature of the lens and reason for its use (ii) Where should the palmist place/hold the lens so as to have a real and magnified image of an object ?
(iii) If the focal length of this lens is 10 cm and the lens is held at a distance of 5 cm from the palm, use lens formula to find the position and size of the image.
Answer : (i) The nature of lens used for this purpose is convex lens because it produces a magnified image of the palm.
(ii) There are two cases for which a real and magnified image of object is obtained in convex lens :
1. When the object is placed at focus of the lens.
2. When the object is placed between focus and centre of curvature of the lens.
(iii) Given, f = 10 cm
u = – 5 cm

The image is formed 10 cm away from the lens on the same side of the object and would be enlarged, virtual and erect.

Question. An object is placed at a distance of 60 cm from a concave lens of focal length 30 cm.
(a) Use lens formula to find the distance of the image from the lens.
(b) List four characteristics of the image (nature, position, size, erect/inverted) formed by the lens in this case.

(b) So, the image formed will be virtual, erect, small in size and image will be formed between F1 and O.

Question. A 6 cm tall object is placed perpendicular to the principal axis of a concave mirror of focal length 30 cm. The distance of the object from the mirror is 45 cm. Use mirror formula to determine the position, nature and size of the image formed. Also draw labelled ray diagram to show the image formation in this case.
Answer : Given, Height of the object h0 = 6 cm
Focal length, f = – 30 cm
Object distance, u = – 45 cm
Image distance, v = ?
Height of image, hi = ?
We have,

Question. Analyse the following observation table showing variation of image-distance (v) with object-distance (u) in case of a convex lens and answer the questions that follow without doing any calculations :

(a) What is the focal length of the convex lens ? Give reason to justify your answer.
(b) Write the serial number of the observation which is not correct. On what basis have you arrived at this conclusion ?
(c) Select an appropriate scale and draw a ray diagram for the observation at S. No. 2. Also find the approximate value of magnification.
Answer : (a) From the observation 3, the radius of curvature of the lens is 40 cm as distance of object and the distance of the image is same.

(b) S. No. 6 is not correct, as for this observation the object distance is between focus and pole and in such cases, the image formed is always virtual, but in this case real image is forming as the image distance is positive. hence, v should be negative.

Question. (a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual, state the type of the mirror and also draw a ray diagram to justify your answer. Write one use such mirrors are put to and why.
(b) Define the radius of curvature of spherical mirrors. Find the nature and focal length of a spherical mirror whose radius of curvature is + 24 cm.
Answer : (a) The type of the mirror is convex mirror. (diverging mirror)
The ray diagram is shown below :

Use of convex mirror : Convex mirror is used as rear view mirror in vehicles as it always produces virtual, erect and diminished image of an object.  So, images of vehicles over a wide area can be seen easily in it.
(b) Radius of curvature : The distance between the centre of curvature and pole of a spherical mirror is called radius of curvature.

Question.Analyse the following observation table showing variation of image distance (v) with object distance (u) in case of a convex lens and answer the questions that follow, without doing any calculations :

(a) What is the focal length of the convex lens ? Give reason in support of your answer.
(b) Write the serial number of that observation which is not correct. How did you arrive at this conclusion ?
(c) Take an appropriate scale to draw ray diagram for the observation at S. No. 4 and find the approximate value of magnification.
Answer : (a) From S. No. 3, we can say that the radius of curvature is 30 cm because when an object is placed at the centre of curvature of a convex lens, its image is formed on the other side of the lens at the same distance from the lens. And, we also know that focal length is half of the radius of curvature.
Therefore, focal length of the lens is + 15 cm.
(b) S. No. 6 is not correct as the object distance is between focus and optical centre, and in such cases, the image formed is always virtual. But in this case, a real image is formed as the image distance is positive. Therefore, v should be negative.
(c) Approximate value of magnification for object distance – 20 cm and image distance + 60 cm is – 3.

Question. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained ? Find the size and the nature of the image.
Answer : Object distance, u = – 27 cm
Object height, h1 = 7 cm
Focal length, f = – 18 cm
According to the mirror formula,

So, the screen should be placed at a distance of 54 cm in front of the given mirror.
Magnification produced by a mirror,

The negative value of magnification indicates that the image formed is real.
Also,

The negative value of image height indicates that the image formed is inverted.

Question. (a) To construct a ray diagram we use two rays which are so chosen that it is easy to know their directions after reflection from the mirror. List two such rays and state the path of these rays after reflection in case of concave mirrors. Use these two rays and draw ray diagram to locate the image of an object placed between pole and focus of a concave mirror.
(b) A concave mirror produces three times magnified image on a screen. If the object is placed 20 cm in front of the mirror, how far is the screen from the object ?
(a) The following rays of light are usually used to locate the images formed by a concave mirror :
The incident ray passess through the centre of curvature : In this case, light after reflecting from the concave mirror moves back along the same path.

The ray incident obliquely to the principal axis : In this case, the incident ray will be reflected back by the reflecting surface of the concave mirror obliquely, making equal angles with the principal axis.

When the object is placed between pole and focus of the concave mirror, image is formed behind the mirror which is virtual, erect and magnified.

Question. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.
Object distance, u = – 20 cm
Object height, h = 5 cm
Radius of curvature, R = 30 cm
We have R = 2 × f
Focal length, f = 15 cm
According to the mirror formula,

The positive value of v indicates that the image is formed behind the mirror.
Magnification produced by a mirror,

The positive value of magnification indicates that the image formed is virtual and erect.
Magnification produced by a mirror

The positive value of image height indicates that the image formed is erect. Therefore, the image formed is virtual, erect and diminished.

Question. (a) Why is the magnification produced by a concave lens always less than 1 ?
(b) You are provided with two lenses of focal lengths 10 cm and 20 cm. Which of the two lenses would you suggest to obtain greater convergence of refracted light ? Justify your choice.
(c) An image 2/3rd the size of object is formed by a convex lens at a distance of 12 cm from it. Find the focal length of the lens.
Answer : (a) Since the image formed by a concave lens is always smaller than the object. So, the magnification (m) produced by the concave lens is always less than 1.
(b) A convex lens of short focal length has more converging power as it bends the light rays through large angle after refraction as compared to a convex lens having large focal length

Therefore, the convex lens of focal length 10 cm will have greater convergence of refracted light as compared to the convex lens of focal length 20 cm.
(c) For convex lens,

Question. (a) A concave lens is called a diverging lens. Explain this property with the help of diagram.
(b) For a concave mirror draw a ray diagram to show the reflected ray when the ray of light incident obliquely on the pole of mirror.
(c) What is the difference between virtual images produced by concave, plane and convex mirrors ?
Answer : (a) A beam of light from an object at infinity, parallel to the principal axis, falls on a concave lens. After refraction through it, the light appears to come from a fixed point on the same side of an object as shown, i.e., the concave lens spreads out parallel beam of light. Due to this property, the concave lens is called a diverging lens

(c) Difference between virtual image produced by :
(i) Concave mirror : magnified
(ii) Plane mirror : same size
(iii) Convex mirror : diminished

Question. State the laws that are followed when light is refracted by lenses. Draw a ray diagram to show formation of image by a concave lens. List any two characteristics of the image formed. The magnification produced by a concave lens is +0.5. What does this mean ?
(a) The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
(b) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media.

Image formed above is virtual and diminished. Magnification is +0.5 it means size of the image formed is half of the object.

Question. (a) Define the following terms in the context of spherical mirrors :
(i) Pole (ii) Centre of curvature
(iii) Radius of curvature (iv) Principal axis
(b) Draw ray diagrams to show the principal focus of
(i) a concave mirror, and (ii) a convex mirror.
(c) In the following diagram, MM’ is a concave mirror and AB is an object. Draw on your answer sheet a ray diagram to show the formation of image of this object.

(a) Definitions :
(i) Pole – The centre of the reflecting surface of the spherical mirror.
(ii) Centre of curvature – The centre of the sphere of which mirror forms a part.
(iii) Radius of curvature – The radius of the sphere of which mirror forms a part.
(iv) Principal axis – An imaginary straight line passing through the pole and the centre of curvature of the mirror.

Question. Analyse the following observation table showing variation of image-distance (v) with object-distance (u) in case of a convex lens and answer the questions that follow without doing any calculations :

(a) What is the focal length of the convex lens ? State reason for your answer.
(b) For what object-distance (u) is the corresponding image-distance (v) not correct ? How did you arrive at this conclusion ?
(c) Choose an appropriate scale to draw a ray diagram for the observation at S. No. 4 and find the approximate value of magnification.
Answer : (a) Observation no. 3, indicates u = – 20 cm, v = + 20 cm
It suggests that object is at 2f
2f = 20

Therefore f = + 10 cm
(b) Observation no. 6, because, here :
u = – 9 cm
Thus object is between ‘O’ and ‘F’
Hence, image distance should be negative not positive.

Question. Suppose you have three concave mirrors A, B and C of focal lengths 10 cm, 15 cm and 20 cm. For each concave mirror you perform the experiment of image formation for three values of object distance of 10 cm, 20 cm and 30 cm. Giving reason answer the following :
(a) For the three object distances, identify the mirror/ mirrors which will form an image of magnification – 1.
(b) Out of the three mirrors identify the mirror which would be preferred to be used for shaving purposes/makeup.
(c) For the mirror B draw ray diagram for image formation for object distances 10 cm and 20 cm.
Answer : (a) In case of concave mirror, a real and inverted image of same size is formed as that of object,
when object is placed at a distance of 2F. Hence, in case of mirror A when object is placed at 20 cm, and in case of mirror B, when object is placed at 30
cm, the image formed will be of same size as that of object. Thus, magnification in both these cases will be –1.
(b) The mirror C, will focal length of 20 cm will be preferred to be used for shaving or makeup purpose. As within this focal length, enlarged and erect image will be formed.

Question. At what distance from a concave lens of focal length 20 cm a 6 cm tall object be placed so as to obtain its image at 15 cm from the lens ? Also calculate the size of the image formed.
Draw a ray diagram to justify your answer for the above situation and label it.

Answer : Given : f = – 20 cm, h1 = 6 cm, v = – 15 cm, u = ?

Question: “A convex lens can form a magnified erect as well as magnified inverted image of an object placed in front of it”. Draw ray diagram to justify this statement stating the position of the object with respect to the lens in each case.
An object of height 4 cm is placed at a distance of 20 cm from a concave lens of focal length 10 cm. Use lens formula to determine the position of the image formed.

Question: The image of a candle flame placed at a distance of 30 cm from a spherical lens is formed on a screen placed on the other side of the lens at a distance of 60 cm from the optical centre of the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 3 cm, find the height of its image.
Given that u = –30 cm, v = 60 cm, h = 3 cm Lens Formula :

Question: (a) State the laws of refraction of light. Explain the term absolute refractive index of a medium and write an expression to relate it with the speed of light in vacuum.
(b) The absolute refractive indices of two media A and B are 2.0 and 1.5 respectively. If the speed of light in medium B is 2 × 108 m/s, calculate the speed of light in
(i) vacuum
(ii) medium A
Answer: (a) Laws of refraction of light :
(i) THe incident ray, the refracted ray and the normal to the interface of two transparent media at the point incidence, all lie in the same plane.
(ii) The ratio of sine of angle of incidence to the sine of the angle of refraction is constant, for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction.
sini/sinr= constant, where i is the angle of incidence and r is the angle of refraction. This constant value is called refractive index of the second medium with respect to the first.

Question: At what distance from a concave lens of focal length 25 cm a 10 cm tall object be placed so as to obtain its image at 20 cm from the lens. Also calculate the size of the image formed. Draw a ray diagram to justify your answer for the above situation and label it.
Answer: Focal length of concave lens , f = – 25 cm
Image distance, v = –20 cm
Height of the object, h = 10 cm
Now, from lens formula,

Question: (a) Explain the following terms related to spherical lenses:
(i) optical centre
(ii) centres of curvature
(iii) principal axis (iv) aperture
(v) principal focus (vi) focal length
(b) A converging lens has focal length of
Answer: (a) (i) Optical centre : The centre point of a lens is known as the optical centre. It always lies inside the lens. A light beam passing through the
optical centre without any deviation.
(ii) Centre of curvature : It is dened as the centre of the sphere of which the lens is originally a part of. Because the spherical lens consists of two spherical surfaces, the lens has two centre of curvature.
(iii) Principal axis : A straight line passing through the optical centre and principal focus of a spherical lens. This line is called the principal axis.
(iv) Aperture : The diameter of the refiecting surface of spherical lens is called its aperture.
(v) Principal focus : A number of rays parallel to the principal axis are falling on a lens.
These rays, after refraction from the lens, are appearing to converge to or diverge from a point on the principal axis. This point on the principal axis is called the principal focus of the lens.
(vi) Focal length : The distance between the optical centre and the principal focus of a spherical lens is called the focal length. It is represented by the letter f.
(b) Given f = 12 cm, v = 48 cm, u = ?

Question: One half of a convex lens of focal length 10 cm is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of 30 cm from the lens? Draw a ray diagram to justify your answer.
A 4 cm tall object is placed perpendicular to the principal axis of a concave lens of focal length  20 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image.
Yes, the lens will produce an image of complete object.

Question: The image of a candle flame placed at a distance of 45 cm from a spherical lens is formed on a screen placed at a distance of 90 cm from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 2 cm, find the height of its image.
Answer: Given that u = –45 cm, v = +90 cm, h = 2 cm (as the image is formed on the screen, the image is real and hence image is formed by convex lens on
the other side of the lens).

Question: A 4 cm tall object is placed perpendicular to the principal axis of convex lens of focal length 24 cm. The distance of the object from the lens is 16 cm. Find the position, size and nature of the image formed, using the lens formula.

Question: List the sign conventions that are followed in case of refraction of light through spherical lenses. Draw a diagram and apply these conventions in determining the nature and focal length of a spherical lens which forms three times magnified real image of an object placed 16 cm from the lens.
Answer: For lenses, we follow sign convention, similar to one used for spherical mirrors. We apply the rules for signs of distances, except that all measurements are taken from the optical centre of the lens.

Spherical lens is convex lens or converging lens offocal length 12 cm.

Question: With the help of a ray diagram state what is meant by refraction of light. State Snell’s law for refraction of light and also express it mathematically.
The refractive index of air with respect to glass is 2/3 and the refractive index of water with respect to air is 4/3. If the speed of light in glass is 2 × 108 m/s, find the speed of light in (a) air, (b) water.
(a) When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.
The ratio of sine of angle of incidence to the sine of the angle of refraction is constant, for the light of a given colour and for the given pair of media.

Question: (a) Under what condition with a glass lens placed in a transparent liquid become invisible.
(b) Describe and illustrate with a diagram, how we should arrange two converging lenses so that a parallel beam of light entering one lens emerges as a parallel beam aftr passing through the second lens.
(c) An object is placed at a distance of 3 cm from a concave lens of focal length 12 cm.Find the (i) position and (ii) nature of the image formed.
Answer: (a) If the refractive index of glass lens is equal to the refractive index of liquid then of the glass lens is placed in a transparent liquid will become
invisible.
(b) Suppose we have two converging lens of focal lengths f1 and f2. We will keep the two converging lens at a distance of f1 + f2 so that a parallel beam of
light entering one lens emerges as a parallel beam after passing through the second lens.

Here the focus of the two lenses should coincide.
(c) (i) Focal length of concave lens, f = –12 cm Object distance, u = –3 cm
Image distance, v = ?
Using lens formula,

So, the image is formed at 2.4 cm from the concave lens.
(ii) Using magnification formula,

Since m is +ve and magnitude of m is less than 1, so the image formed is virtual and diminished.

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