RAY OPTICS

PREVIOUS YEAR BOARD EXAM QUESTIONS

(2007-2016)
1 MARK QUESTIONS
1. A glass lens of refractive index 1.5 is placed in a
trough of liquid. What must be the refractive index of
the liquid in order to make the lens disappear?

2. How does the angle of minimum deviation of a glass

prism vary, if the incident violet light is replaced with
red light?

3. Why does the bluish colour predominate in a clear

sky?

4. Under what condition, does a biconvex lens of glass,

having a certain refractive index, act as a plane glass
sheet, when immersed in a liquid?

5. Why should be the objective and eye piece have

short focal lengths in a compound microscope?
6. Write the relationship between angle of incidence,
“i”, angle of prism , “a”, and angle of minimum
deviation for a triangular prism.

7. A converging lens is kept coaxially in contact with a

diverging lens – both the lenses being of equal focal
lengths. What is the focal length of the combination?

8. When light travels from a rarer to a denser medium,

the speed decreases. Does this decrease in speed imply
a decrease in the energy carried by the light wave?
Justify your answer.

9. How does focal length of a lens change when red light

incident on it is replaced by violet light? Give reason for
your answer.
10. An object is placed in front of convex lens made of
glass. How does the image distance vary if the refractive
index of the medium is increased in such a way that still
it remains less than the glass?
11. What is dispersion of light? What is its cause?
12. “Violet colour is seen at the bottom of the
spectrum when white light is dispersed by a prism” –
Justify.
13. Why can’t we see clearly through fog? Name the
phenomenon responsible for it.
14. Explain briefly, how the focal length of a convex lens
changes with increase in wavelength of incident light.
15. Give one reason for using a concave mirror, rather
than a lens, as an objective in a reflecting type
telescope.

16. A biconvex lens made of a transparent material of

refractive index 1.25 is immersed in water of refractive
index 1.33. Will the lens behave as a converging or a
diverging lens? Give reason.

17. A convex lens is placed in contact with a plane

mirror. A point object at a distance of 20 cm on the axis
of this combination has its image coinciding with itself.
What is the focal length of the lens ?

18. A ray of light falls on a transparent sphere with

centre C as shown in the figure. The ray emerges from
the sphere parallel to the line AB. Find the angle of
refraction at A if refractive index of the material of the
sphere is √3.

19. State the phenomenon of light involved in the

formation of coloured soap bubbles.

20. Write the expression for total magnification when

the image is formed at infinity.

21. Justify- “Astronomers prefer to use telescopes with

large objective diameters to observe astronomical
objects”.

22. A ray of light incident on an equilateral glass prism

of refractive index √3, moves parallel to base of prism,
inside it. Find the angle of incidence for this ray.
23.

24. “When a monochromatic light travels from one

medium to another, its wavelength changes, but
frequency remains same”- Explain.

25. Write the factors by which the resolving power of a

telescope can be increased.

26. When an object is placed between f and 2f of a

concave mirror, would the image formed be (i) real or
virtual and (ii) diminished or magnified?

27. When light travels from an optically denser medium

to a rarer medium, why does the critical angle of
incidence depend on the colour of light?
28. For the same angle of incidence, the angle of
refraction in two media A and B are 250 and 350
respectively. In which medium is the speed of light less?

29. The line AB in the ray diagram represents a lens.

State whether the lens is convex or concave.

30. Mention the factors by which the resolving power of

a microscope can be increased.

31. The radii of curvature of both the surfaces of a lens

are equal. If one of the surfaces is made plane by
grinding, how will the focal length and power of the
lens change?
32. The focal length of an equiconvex lens is equal to
the radius of curvature of either face. What is the
refractive index of the material of the lens?

33. The line AB in the ray diagram represents a lens.

State whether the lens is convex or concave.

2 MARK QUESTIONS
1. A convex lens of refractive index 1.5 has a focal
length of 18 cm in air. Calculate the change in its focal
length when it is immersed in water of refractive index
4/3.
2. Define resolving power of a compound microscope.
How does the resolving power of a compound
microscope change, when:

(i) refractive index of the medium between the object

and objective lens increases ?

(ii) wavelength of the radiation used is increased ?

3. Draw a schematic arrangement of a reflecting type

telescope, showing how the rays coming from a distant
object are received at eye piece. State two advantages
of this telescope over a refracting telescope.

4. A ray of light passing through an equilateral

triangular glass prism from air undergoes minimum
deviation when angle of incidence is 3/4th of the angle
of prism. Calculate the speed of light in the prism.

5. Draw a labeled ray diagram of an astronomical

telescope in the near point position. Write the
expression for its magnifying power.

6. A ray of light is incident on an equilateral glass prism,

with refractive index = √3, moves parallel to the base
line of prism inside it. Find the angle of incidence of this
ray.

7. A convex lens of focal length 25 cm is placed coaxially

in contact with a concave lens of focal length 20 cm.
Determine the power of combination. Will the system
be converging or diverging in nature?

8. A ray PQ incident on refracting surface BA is refracted

in prism BAC, and emerges from other refracting face
AC as RS, such that AQ=AR. If refractive index of
material is 1.732 and angle of prism is 60, find the angle
Ѳ.

9. The radii of curvature of the faces of a double convex

lens are 10 cm and 15 cm. If focal length of the lens is 12
cm, find the refractive index of the material of the lens.
10. A screen is placed at a distance of 100 cm from an
object. The image of the object is formed on screen by a
convex lens for two different location of lens separated
by 20 cm. Calculate the focal length of lens used.

11. Calculate the speed of light in a medium whose

critical angle is 450. Does critical angle for a given pair of
media depend on the wavelength of incident light? Give
reason.

12.
13. Calculate the value of θ, for which light incident
normally on face AB grazes along the face BC. μg = 3/2
μw = 4/3.

14. An object is placed in front of right angled prism

ABC in two positions as shown. The prism is made of
crown glass with critical angle of 410. Trace the path of
the two rays from P & Q.

15. Define magnifying power of a compound

microscope. Why is a compound microscope preferred
over a simple microscope?
16. You are given three lenses of power 0.5 D, 4 D and
10 D to design a telescope.

(a). Which lenses should be used as objective and

eyepiece? Give reason.

(b). Why is the aperture of objective, preferred to be

large?

17. Light from a point source in air falls on a convex

spherical glass surface of refractive index 1.5, and radius
of curvature 20 cm. The distance of light source from
glass surface is 100 cm. At what position is image
formed?

18. A convex lens is placed over a plane mirror. A pin is

now positioned so that there is no parallax between the
pin and its image formed by this lens-mirror
combination. How will you use this observation to find
focal length of a lens? Justify.

19. A ray of light incident normally on one face of a right

isosceles prism undergoes total internal reflection.
What should be the minimum refractive index of glass
for this condition? Give relevant calculations.
20. Which two aberrations do objective lenses of
refracting telescope suffer from? How are these
overcome by a reflecting type telescope?

21. Account for following:

(a). A convex lens when immersed in a medium whose
refractive index is more than that of the material of
the lens, behaves like a diverging lens.
(b). Both the objective and the eyepiece of a
compound microscope have short focal lengths.

22. Use the mirror formula to show that the virtual

image produced by a convex mirror is always
diminished in size and is located between the focus and
the pole.

23. The radii of curvature of the faces of a double

convex lens are 10 cm and 15 cm. Its focal length is 12
cm. Calculate the refractive index of the material of the
lens.

24. The total magnification produced by a compound

microscope is 20. The magnification produced by the
eye piece is 5. The microscope is focused on a certain
object. The distance between the objective and
eyepiece is observed to be 14 cm. If least distance of
distinct vision is 20 cm, calculate the focal length of the
objective and the eye piece.

25. Write the main considerations required in selecting

the objective and eyepiece lenses in order to have large
magnifying power and high resolution of the telescope.

26. A compound microscope has an objective of focal

length 1.25 cm and eyepiece of focal length 5 cm. A
small object is kept at 2.5 cm from the objective. If the
final image formed is at infinity, find the distance
between the objective and the eyepiece.

27. Figure shows a ray of light passing through a prism.

If the refracted ray QR is parallel to the base BC, show
that (i). r1 = r2 = A/2, (ii). angle of minimum deviation,
Dm = 2i – A.
28. A double convex lens having both faces of the same
radius of curvature has refractive index 1.55. Find out
the radius of curvature of the lens required to get the
focal length of 20 cm.

29. The sum of focal lengths of the two lenses of a

refracting telescope is 105 cm. The focal length of one
lens is 20 times that of the other. Determine the total
magnification of the telescope when the final image is
formed at infinity.

30. Write the conditions for observing a rainbow. Show,

by drawing suitable diagrams, how one understands the
formation of a rainbow.

31. In the accompanying diagram, the direct image

formed by the lens (f = 10cm) of an object placed of O
and that formed after reflection from the spherical
mirror are formed at the same point. What is the radius
of curvature of the mirror?

32. How does the resolving power of a compound

microscope get affected on:

(i). decreasing the diameter of its objective?

(ii). increasing the focal length of its objective?

33. A light beam is incident on boundary between two

transparent media. At a particular angle of incidence,
the reflected ray is perpendicular to refracted ray.
Obtain an expression for angle of incidence. Does this
angle depend on wavelength of light used?

34. A luminescent object is placed at a depth “d” in an

optically denser medium of refractive index “µ”. Prove
that the radius “r” of the base of cone of light from the
object that can emerge out is
35.

36. Draw a ray diagram to show the image formation by

a concave mirror when the object is kept between its
focus and pole. Using this diagram, obtain the
expression for magnification of image obtained.

37. Why does white light disperse when passed through

a glass prism? Using lens maker’s formula, show how
the focal length of a given lens depends upon the colour
of light incident on it.

38. You are given two converging lenses of focal lengths

1·25 cm and 5 cm to design a compound microscope. If
it is desired to have a magnification of 30, find out the
separation between the objective and the eyepiece.

39. A biconvex lens of glass of refractive index 1·5

having focal length 20 cm is placed in a medium of
refractive index 1·65. Find its focal length. What should
be the value of the refractive index of the medium in
which the lens should be placed so that it acts as a
plane sheet of glass?

40. A beam of light converges at a point P. Now a lens is

placed in the path of the convergent beam 12 cm from
P. At what point does the beam converge if the lens is

(i). a convex lens of focal length 20 cm,

(ii). a concave lens of focal length 16 cm?

41. A ray of light incident on one of the faces of a glass

prism of angle ‘A’ has angle of incidence 2A. The
refracted ray in the prism strikes the opposite face
which is silvered, the reflected ray from it retracing its
path. Trace the ray diagram and find the relation
between the refractive index of the material of the
prism and the angle of the prism.
42.

43. A screen is placed 90 cm away from an object. The

image of the object on the screen is formed by a convex
lens at two different locations separated by 20 cm.
Determine the focal length of the lens.

44. Assume that the light of wavelength 6000 Å is

coming from a star. Find the limit of resolution of a
telescope whose objective has a diameter of 250 cm.

45. Explain the basic differences between the

construction and working of a telescope and a
microscope.

46. An object is placed 40 cm from a convex lens of focal

length 30 cm. If a concave lens of focal length 50 cm is
introduced between the convex lens and the image
formed such that it is 20 cm from the convex lens, find
the change in the position of the image.

3 MARK QUESTIONS
1. Define the term 'resolving power' of an astronomical
telescope. How does it get affected on:

(i). increasing the aperture of the objective lens?

(ii).increasing the wavelength of the light used?

Justify your answer in each case.

2. Draw a schematic diagram of a single optical fibre

structure. On what principle does such a device work?
Explain the mechanism of propagation of light signal
through an optical fibre.

3. A double convex lens of glass of refractive index 1.6

has its both surfaces of equal radii of curvature of 30 cm
each. An object of height 5 cm is placed at a distance of
12.5 cm from the lens. Calculate the size of the image
formed.
4. Define power of a lens. Write its unit. Deduce the
relation = + for two lenses kept in contact
coaxially.

5. A small bulb(assumed to be a point source) is placed

at the bottom of a tank containing water to the depth
of 80 cm. Find out the area of the surface of water
through which light from bulb can emerge. Take the
value of refractive index of water to be 4/3.

6. Draw a ray diagram showing the image formation by

a compound microscope. Hence, obtain the expression
for total magnification when the image is formed at
infinity.

7. (i). Draw a neat labeled ray diagram of an

astronomical telescope in normal adjustment.
Explain briefly its working.

(ii). An astronomical telescope uses two lenses of

powers 10 D and 1 D. What is its magnifying power in
normal adjustment?

8. An illuminated object and a screen are placed 90 cm

apart. Determine the focal length and nature of the lens
required to produce a clear image on the screen, twice
the size of the object.

9. A compound microscope consists of an objective of

focal length 1cm and eye piece of focal length 5cm
separated by 12.2cm.

(a). At what distance from the objective should an

object be placed so that the final image is formed at
least distance of distinct vision?

(b). Calculate the angular magnification in this case.

10. A ray of monochromatic light is incident on one face
of an equilateral prism, at an angle 3/4th of the angle of
prism. If the ray passes symmetrically through the
prism, find the angle of minimum deviation and
refractive index of material of prism.
11. (a). Write the necessary conditions for the
phenomenon of total internal reflection to take
place.
(b).Write the relation between the refractive index
and critical angle for a given pair of optical media.
 (c). Name any two phenomenon based on total
internal reflection.
12. (a). Draw the schematic diagram of a compound
microscope, when image is formed at distance of
distinct vision.
(b). Write the expression for resolving power of a
compound microscope? How can it be increased?
13. (a). Using mirror formula, explain why does a
convex mirror always produce a virtual image.
(b). Calculate the distance of an object of height h,
from a concave mirror of radius of curvature 20 cm,
so as to obtain a real image of magnification 2. Find
the location of image, also.
14. Three rays of different colors, fall normally on one
of the sides of an isosceles right angled prism. The
refractive index of prism, for these rays are 1.39,
1.47 and 1.52 respectively. Trace the path of three
rays. Find out which of these rays undergoes total
internal reflection, and which one gets refracted
through opposite side. Justify with calculations.
15. An object ‘O’ is placed 15 cm in front of a convex
lens L1 of focal length 20 cm and the final image is
formed at ‘I’ at a distance of 80 cm from the second lens
L2. Find the focal length of the lens L2. Draw the ray
diagram for this arrangement also.

16.(a). Draw a ray diagram when incident light falls

normally on one of the two equal sides of an isosceles
right prism having refractive index √3.

(b). For a glass prism, the angle of minimum deviation

is equal to angle of prism. Calculate the angle of
prism, given the refractive index is √3.

17. Name the phenomenon based on which optical

fibres work. Draw the labeled diagram of an optical
fibre, and show how light propagates through optical
fibre based on this phenomenon.
18. Draw a ray diagram to show the passage of a ray of
light through a triangular prism. Use this diagram to
obtain the relation for the refractive index of the
material of the prism in terms of the angle of minimum
deviation and the angle of the prism.
19. A convex lens of focal length 20 cm is placed
coaxially with a convex mirror of radius of curvature 20
cm. The two are kept at 15 cm from each other. A point
object lies 60 cm in front of the convex lens. Draw a ray
diagram to show the formation of the image by the
combination. Determine the nature and position of the
image formed.

20. (a). A mobile phone lies along the principal axis of a

concave mirror. Show, with the help of a suitable
diagram the formation of its image. Explain why
magnification is not uniform.

(b). Suppose, the lower half of the concave mirror's

reflecting surface is covered with an opaque material.
What effect this will have on the image of the object?
Explain.

21. A point object O is kept at a distance of 30 cm from

a convex lens of power +4D towards its left. It is
observed that when a convex mirror is kept on the right
side at a distance of 50 cm from the convex lens, the
image of the object O formed by the lens-mirror
combination coincides with the object itself. Calculate
the focal length of the convex mirror.

22. An object is placed at a distance of 15 cm, from a

convex lens of focal length 10cm. On the other side of
the lens, a convex mirror is placed such that its distance
from the lens, equals the focal length of the lens. The
image formed by this combination is observed to
coincide with object itself. Find the focal length of
convex mirror.

23. Two convex lenses of equal focal length but of

aperture A1 and A2 (A1 > A2) are used as objective lenses
in two astronomical telescopes having identical
eyepieces. Compare the ratio of their magnifying
power(normal adjustment), resolving power and
intensity of images formed.

Which one the two telescopes should be preferred?

Why?

24. A 5 cm long needle is placed 10 cm from a convex

mirror of focal length 40 cm. Find the position, size and
nature of image. What happens to size of image when
the needle is moved farther away from the mirror?
25. For a thin convex lens, define the term linear
magnification. Hence, draw a plot showing variation of
linear magnification with image distance. How can this
graph be used for finding focal length of lens?

26.Using mirror equation, show that:

(a). an object placed between f and 2f of a concave

mirror ,produces a real image beyond 2f.

(b). an object placed between pole and focus of a

concave mirror produces enlarged virtual image.

(c). a convex mirror always produces a virtual image

independent of location of object.

27. A giant refracting telescope at an observatory has

an objective lens of focal length 15 m. If an eyepiece of
focal length 1 cm is used, find the angular magnification
of telescope.

If this telescope is used to see moon, what is the

diameter of image of moon formed by objective lens?
The diameter of moon is 3.42 x 106 m and radius of
lunar orbit is 3.8 x 108 m.
28. A compound microscope uses an objective lens of
focal length 4 cm and eyepiece lens of focal length 10
cm. An object is placed at 6 cm from objective lens.
Calculate the length and magnifying power of
compound microscope.

29.

30. How does the resolving power of a compound

microscope get affected, when:

(i). focal length of the objective is decreased.

(ii). the wavelength of light is increased

Give reasons to justify your answer.

31. Define the term ‘critical angle’ for a pair of media. A

point source of monochromatic light ‘S’ is kept at the
centre of the bottom of a cylinder of radius 15.0 cm.
The cylinder contains water (refractive index 4/3) to a
height of 7.0 cm. Draw the ray diagram and calculate
the area of water surface through which the light
emerges in air.

32. Which two of the following lenses L1, L2 and L3 will

you select as objective and eyepiece for constructing
best possible (i) telescope (ii) microscope? Give reason
to support your answer.

Lens Power (P) Aperture (A)

L1 6D 1 cm

L2 3D 8 cm

L3 10D 1 cm

33. Find out the relation between the refractive index

(µ) of the glass prism and A, for the case when the
angle of prism (A) is equal to the angle of minimum
deviation (dm). Hence obtain the value of the refractive
index for angle of prism A = 600.

34. Obtain the expression for the minimum separation

between the two points seen as distinct in a
microscope. What is its relation with the resolving
power?

35. An object is placed 15 cm in front of a convex lens of

focal length 10 cm. Find the nature and position of the
image formed. Where, should a concave mirror of
radius of curvature 20 cm be placed so that the final
image is formed at the position of the object itself?

36. Two thin convex lenses L1 and L2 of focal lengths f1

and f2 respectively, are placed coaxially in contact. An
object is placed at a point beyond the focus of lens L1.
Draw a ray diagram to show the image formation by the
combination and hence derive the expression for the
focal length of the combined system.

5 MARK QUESTIONS
1. (a). Derive the relation between the focal length of a
convex lens in terms of the radii of curvature of the
two surfaces and refractive index of its material.
Write the sign conventions and two assumptions
used in the derivation of this relation.
 (b).A convex lens of focal length 40 cm and a concave
lens of focal length — 25 cm are kept in contact with
each other. What is the value of power of this
combination?

2. (a). For a ray of light travelling from a denser medium

of refractive index n1 to a rarer medium of refractive
index n2, prove that n2/n1= sin ic, where ic is the
critical angle of incidence for the media.

(b).Explain with the help of a diagram, how the above

principle is used for transmission of video signals using
optical fibres.
3. (a). Draw a ray diagram to show the working of a
compound microscope. Deduce an expression for the
total magnification when the final image is formed at
the near point.
(b). In a compound microscope, an object is placed at
a distance of 1.5 cm from the objective of focal length
1.25 cm. If the eye piece has a focal length of 5 cm and
the final image is formed at the near point, estimate
the magnifying power of the microscope.
4. (a). How is working of a telescope different from that
of a microscope?

(b). The focal lengths of objective and eyepiece of a

microscope are 1.25 cm and 5 cm respectively. Find
the position of object, relative to objective, in order
to obtain an angular magnification of 30 in normal
adjustment.

5. (a). Define magnifying power of a telescope. Write its

expression.

(b). A small telescope has an objective lens of focal

length 150cm, and an eyepiece of focal length 5 cm. If
this telescope is used to view a 100 m high tower, 3
km away, find the height of final image, when the
image is formed at a distance of 25 cm away from
eyepiece.

6. Draw a graph showing the variation of angle of

deviation ‘δ’ with that of angle of incidence ‘i’ for a
monochromatic ray of light passing through a glass
prism of refracting angle ‘A’. What do you interpret
from the graph? Write a relation showing the
dependence of angle of deviation on angle of incidence
and hence derive the expression for refractive index of
the prism.

7. Draw a ray diagram to show the formation of the real

image of a point object due to a convex spherical
refracting surface, when a ray of light is travelling from
a rarer medium of refractive index μ1 to a denser
medium of refractive index μ2. Hence, derive the
relation between object distance, image distance and
radius of curvature of the spherical surface. Also, obtain
lens makers formula.

8. (a).Explain, with the help of a diagram, how is the

phenomenon of total internal reflection used in :

(i). an optical fibre

(ii). a prism that inverts an image without changing

its size

(b). A right angled prism made from a material of

refractive index is kept in air. A ray PQ is incident
normally on the side AB of the prism as shown. Find
(in terms of ) the maximum value of upto which
this incident ray necessarily undergoes total internal
reflection at the face AC of the prism.
9. (i). Derive the mirror formula which gives the relation
between f, v and u. What is the corresponding formula
for a thin lens?

(ii).Calculate the distance d, so that a real image of an

object at O, 15cm in front of a convex lens of focal
length 10cm be formed at the same point O. The
radius of curvature of the mirror is 20cm. Will the
image be inverted or erect?

10. (a). A point-object is placed on the principal axis of a

convex spherical surface of radius of curvature R,
which separates the two media of refractive indices n1
and n2 (n2 > n1). Draw the ray diagram and deduce
the relation between the distance of the object (u),
distance of the image (v) and the radius of curvature
 (R) for refraction to take place at the convex spherical
surface from rarer to denser medium.

(b). Use the above relation to obtain the condition on

the position of the object and the radius of curvature
in terms of n1 and n2 when the real image is formed.

11. A biconvex lens with its two faces of equal radius of

curvature R is made of a transparent medium of
refractive index µ1. It is kept in contact with a medium
of refractive index µ2 as shown in the figure.

(a). Find the equivalent focal length of the

combination.

(b). Obtain the condition when this combination acts

as a diverging lens.

(c).Draw the ray diagram for the case µ1 > (µ2 + 1) / 2,

when the object is kept far away from the lens. Point
out the nature of the image formed by the system.

(Diagram given in next page)