CHAPTER 9

Ray Optics and Optical Instruments

1. INTRODUCTION TO RAY OPTICS

Objective Qs (1 mark)
1. A ray of light of wavelength 600 nm propagates from air into a medium. If its wavelength
in the medium becomes 400 nm, the refractive index of the medium is:
(a) 1.4
(b) 1.5
(c) 1.6
(d) 1.8
[CBSE 2023]

2. An object is placed at 10 cm in front of a concave mirror of radius of curvature 15 cm.

The position of the image is:
(a) 15 cm
(b) −30 cm
(c) −25 cm
(d) 5 cm
[Delhi Gov. SQP 2022]

For Questions 3-4, two statements are given -one labelled Assertion (A) and other labelled
Reason (R). Select the correct answer to these questions from the options as given below.

(a) If both Assertion and Reason are true and Reason is correct explanation of Assertion.

(b) If both Assertion and Reason are true but Reason is not the correct explanation of
Assertion.

(c) If Assertion is true but Reason is false.

(d) If both Assertion and Reason are false.

3. Assertion (A): Propagation of light through an optical fibre is due to total internal
reflection taking place at the core-cladding interface.
Reason (R): Refractive index of the material of the cladding of the optical fibre is greater
than that of the core.

[CBSE SQP 2023]

4. Assertion (A): A convex mirror cannot form real images.

Reason (R): Convex mirror converges the parallel rays that are incident on it.

[CBSE SQP 2020]

 Case Based Qs 4-5 marks
5. A ray of light travels from a denser to a rarer medium. After refraction, it bends away from
the normal. When we keep increasing the angle of incidence, the angle of refraction also
increases till the refracted ray grazes along the interface of two media. The angle of
incidence for which it happens is called critical angle. If the angle of incidence is
increased further the ray will not emerge and it will be reflected back in the denser
medium. This phenomenon is called total internal reflection of light.
(A) A ray of light travels from a medium into water at an angle of incidence of 18∘ . The
refractive index of the medium is more than that of water and the critical angle for the
interface between the two media is 20∘ . Which one of the following figures best represents
the correct path of the ray of light?

(B) A point source of light is placed at the bottom of a tank filled with water, of refractive
index, 𝜇𝜇, to a depth 𝑑𝑑. The area of the surface of water through which light from the
source can emerge is:
𝜋𝜋𝑑𝑑 2
(a)
2(𝜇𝜇 2 −1)
𝜋𝜋𝑑𝑑 2
(b)
(𝜇𝜇 2 −1)
𝜋𝜋𝑑𝑑 2
(c)
√2�𝜇𝜇 2 −1
2𝜋𝜋𝑑𝑑 2
(d)
�𝜇𝜇 2 −1

(C) For which of the following media, with respect to air, the value of critical angle is
maximum?
(a) Crown glass
(b) Flint glass
(c) Water
(d) Diamond

(D) The critical angle for a pair of two media 𝐴𝐴 and 𝐵𝐵 of refractive indices 2.0 and 1.0
respectively is:
(a) 0∘
(b) 30∘
(c) 45∘
(d) 60∘
 (E) The critical angle of pair of a medium and air is 30∘ . The speed of light in the medium
is:
(a) 1 × 108 ms −1
(b) 1.5 × 108 ms −1
(c) 2.2 × 108 ms −1
(d) 2.8 × 108 ms −1

[CBSE Term-2 2022]

Very Short & Short Qs (1-3 marks)

6. A triangular prism of refracting angle 60∘ is made of a transparent material of refractive
2
index . A ray of light is incident normally on the face 𝐾𝐾𝐾𝐾 as shown in the figure.
√3

Trace the path of the ray as it passes through the prism and calculate the angle of
emergence and angle of deviation.

[CBSE 2019]

7. Under what conditions does the phenomenon of total internal reflection take place? Draw
a ray diagram showing how a ray of light deviates by 90∘ after passing through a right
𝐴𝐴

of an equilateral glass
3 4
prism having refractive index , placed in water of refractive index . Will this ray suffer
2 3
total internal reflection on striking the face AC? Justify your answer.
 [CBSE 2018]

11. 𝐴𝐴 ray 𝑃𝑃𝑃𝑃 incident normally on the refracting face 𝐵𝐵 is refracted in the prism 𝐵𝐵𝐴𝐴𝐵𝐵 made
of material of refractive index 1.5. Complete the path of ray through the prism. From
which face will the ray emerge? Justify your answer.

[CBSE 2016]

12. (A) 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.
(B) Using mirror formula, explain why does a convex mirror always produce a virtual
image.

[CBSE 2016]

13. When an object is placed between 𝑓𝑓 and 2𝑓𝑓 of a concave mirror, would the image formed
be (i) real or virtual, and (ii) diminished or magnified?
[CBSE 2015]

14. Use the mirror equation to show that an object placed between 𝑓𝑓 and 2𝑓𝑓 of a concave
mirror produces a real image beyond 2𝑓𝑓.
[CBSE 2015]

15. How does the refractive index of a transparent medium depend on the wavelength of
incident light used? Velocity of light in glass is 2 × 108 m/s and in air is 3 × 108 m/s. If
the ray of light passes from glass to air, calculate the value of critical angle.
[CBSE 2015]

16. (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 will this have on the image of the object? Explain.
 𝐴𝐴

of an isosceles
right angled prism 𝐴𝐴𝐴𝐴. The refractive indices of the glass prism for the two rays ' 1 ' and '
2 ' are respectively 1.35 and 1.45. Trace the path of these rays after entering through the
prism.

[CBSE 2014]

18. Two object 𝑃𝑃 and 𝑄𝑄 when placed at different positions in front of a concave mirror of
focal length 20 cm, form real images of equal size. Size of object 𝑃𝑃 is three times the size
of object 𝑄𝑄. If the distance of 𝑃𝑃 is 50 cm from the mirror, find the distance of 𝑄𝑄 from the
mirror.
[CBSE 2020]

19. An object is kept 20 cm in front of a concave mirror having radius of curvature 60 cm.
Find the nature and position of the image formed.
[CBSE 2020]

2. REFRACTION AT SPHERICAL SURFACE AND BY LENSES

Objective Qs (1 mark)
20. A biconcave lens of power 𝑃𝑃 vertically splits into two identical plano-concave parts. The
power of each part will be:
(a) 2P
𝑃𝑃
(b)
2
(c) P
𝑃𝑃
(d)
√2

[CBSE 2020]

Case Based Qs (4 - 5 marks)

21. Read the following paragraph and answer the questions that follow.
A convex or converging lens is thicker at the centre than at the edges. It converges a beam
of light on refraction through it. It has a real focus. Convex lens is of three types: Double
convex lens, Plano convex lens and Concavo-convex lens.

Concave lens is thinner at the centre than at the edges. It diverges a beam of light on
refraction through it. It has a virtual focus. Concave lenses are of three types: Double
concave lens, Plano concave lens and Convexo-concave lens.
When two thin lenses of focal lengths 𝑓𝑓1 and 𝑓𝑓2 are placed in contact with each other along
their common principal axis, then the two lens system is regarded as a single lens of focal
length 𝑓𝑓 and

1 1 1
= +
𝑓𝑓 𝑓𝑓1 𝑓𝑓2

If several thin lenses of focal length 𝑓𝑓1 , 𝑓𝑓2 , … . 𝑓𝑓𝑛𝑛 are placed in contact, then the effective
focal length of the combination is given by

1 1 1 1
= + + ⋯..+
𝑓𝑓 𝑓𝑓1 𝑓𝑓2 𝑓𝑓𝑛𝑛

and in terms of power, we can write

𝑃𝑃 = 𝑃𝑃1 + 𝑃𝑃2 + ⋯ . +𝑃𝑃𝑛𝑛

The value of focal length and power of a lens must be used with proper sign consideration.

(A) Two thin lenses are kept coaxially in contact with each other and the focal length of
the combination is 80 cm. If the focal length of one lens is 20 cm, the focal length of the
other would be:
(a) −26.7 cm
(b) 60 cm
(c) 80 cm
(d) 30 cm

(B) A spherical air bubble is embedded in a piece of glass. For a ray of light passing
through the bubble, it behaves like a:
(a) converging lens

(b) diverging lens

(c) mirror

(d) thin plane sheet of glass

(C) Lens generally used in magnifying glass is:

(a) single concave lens

(b) single convex lens

(c) combination of convex lens of lower power and concave lens of lower focal length
 (d) Planoconcave lens

(D) The magnification of an image by a convex lens is positive only when the object is
placed:

(a) at its focus 𝐹𝐹

(b) between F and 2 F

(c) at 2 F

(d) between F and optical centre

(E) A convex lens of 20 cm focal length forms a real image which is three times
magnified. The distance of the object from the lens is:
(a) 13.33 cm
(b) 14 cm
(c) 26.66 cm
(d) 25 cm

[CBSE SQP 2023]

Very Short & Short Qs (1-3 marks)

22. Show that the least possible distance between an object and its real image in a convex lens
is 4𝑓𝑓, where 𝑓𝑓 is the focal length of the lens.
[CBSE SQP 2023]

23. The focal length of a convex lens made of glass of refractive index (1.5) is 20 cm. What
will be its new focal length when placed in a medium of refractive index 1.25 ? Is focal
length positive or negative? What does it signify?
[CBSE SQP Term-2 2022]

24. 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.
[CBSE SQP 2022, CBSE 2014]

25. (A) An object is placed in front of a converging lens. Obtain the conditions under which
the magnification produced by the lens is (i) negative, and (ii) positive.
(B) A point object is placed at 𝑂𝑂 in front of a glass sphere as shown in the figure. Show
the formation of image by the sphere.

[CBSE Term - 2 2022]

26. An equiconvex lens forms a two times enlarged real image when an object is kept 16 cm
from it. The lens in cut into two identical plano-convex lenses. If the object is again kept
16 cm in front of one of these lenses, then find the nature and position of the image
formed. [CBSE Term- 2 2022]

27. A beam of light converges at a point P. Draw ray diagrams to show where the beam will
converge if:

(A) a convex lens, and

(B) a concave lens is kept in the path of the beam.

[CBSE 2019]

28. A symmetric biconvex lens of radius of curvature 𝑅𝑅 and made of glass of refractive index
1.5 , is placed on a layer of liquid placed on top of a plane mirror as shown in the figure.
An optical needle with its tip on the principal axis of the lens is moved along the axis until
its real, inverted image coincides with the needle itself. The distance of the needle from
the lens is measured to be 𝑥𝑥. On removing the liquid layer and repeating the experiment,
the distance is found to be 𝑦𝑦. Obtain the expression for the refractive index of the liquid in
terms of 𝑥𝑥 and 𝑦𝑦.

[CBSE 2018]

Long Qs (4-5 marks)

29. (A) Draw a ray diagram for the formation of image of a point object by a thin double
convex lens having radii of curvature 𝑅𝑅1 and 𝑅𝑅2 . Hence derive lens maker's formula.
(B) A converging lens has a focal length of 10 cm in air. It is made of a material of
refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal
length.

[CBSE SQP 2023]

30. A point object in air is placed symmetrically at a distance of 60 cm in front of a concave

spherical surface of refractive index 1.5. If the radius of curvature of the surface is 20 cm,
find the position of the image formed.
[CBSE 2023]

31. (A) Define SI unit of power of a lens.

(B) A plane convex lens is made of glass of refractive index 1.5. The radius of curvature
of the convex surface is 25 cm.

(i) Calculate the focal length of the lens.

 (ii) If an object is placed 50 cm is front of the lens, find the nature and position of the
image formed.

[CBSE Term-2 2022]

32. (A) Two thin lenses are placed coaxially in contact. Obtain the expression for the focal
length of this combination in terms of the focal lengths of the two lenses.
(B) A converging lens of refractive index 1.5 has a power 10D. When it is completely
immersed in liquid, it behaves as a diverging lens of focal length 50 cm. Find the
refractive index of the liquid.

[CBSE 2020]

33. A screen is placed 80 cm from an object. The image of the object on the screen is formed
by a convex lens placed between them at two different location separated by a distance
20 cm. Determine the focal length of the lens.
[CBSE 2020]

34. Three lenses of focal length +10 cm, −10 cm and +30 cm are arranged coaxially as in
the figure given below. Find the position of the final image formed by the combination.

[CBSE 2019]

35. (A) A point object ' 𝑂𝑂 ' is kept in a medium of refractive index 𝑛𝑛 in front of a convex
spherical surface of radius of curvature 𝑅𝑅 which separates the second medium of refractive
index 𝑛𝑛2 from the first one as shown in the figure. Draw the ray diagram showing the
image formation and deduce the relationship between the object distance and the image
distance in terms of 𝑛𝑛1 , 𝑛𝑛2 and 𝑅𝑅.

(B) When the image formed above acts as a virtual object for a concave spherical surface
separating the medium 𝑛𝑛2 from 𝑛𝑛1 (𝑛𝑛2 > 𝑛𝑛1 ) draw this ray diagram and write the (similar
to (𝐴𝐴)) relation. Hence, obtain the expression for the Lens Maker's formula.

[CBSE 2015]

Numerical Qs (𝟏𝟏 − 𝟓𝟓 marks)

36. Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is
kept in a medium of refractive index 1.4, to have a power of - 5D?
[CBSE 2019]

37. (A) Monochromatic light of wavelength 589 nm is incident from air on a water surface. If
𝜇𝜇 for water is 1.33, find the wavelength, frequency and speed of the refracted light.
(B) A double convex lens is made of a glass of refractive index 1.55, with both faces of
the same radius of curvature. Find the radius of curvature required, if the focal length is
20 cm.

[CBSE 2017]

38. An equiconvex lens of focal length 𝑓𝑓 is cut into two identical plane convex lenses. How
will the power of each part be related to the focal length of the original lens? A double
convex lens of +5𝐷𝐷 is made of glass of refractive index 1.55 with both faces of equal radii
of curvature. Find the value of its radius of curvature.
[CBSE 2015]

39. In the following diagram, an object 𝑂𝑂 is placed 15 cm in front of a convex lens 𝐾𝐾1 of focal
length 20 cm and the final image is formed at I at a distance of 80 cm from the second
lens 𝐾𝐾2 . Find the focal length of the lens L2 .

[CBSE 2015]

40. 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?
[CBSE 2014]

41. A convex lens of focal length 20 cm is placed co-axially with a concave mirror of focal
length 10 cm at a distance of 50 cm 𝐶𝐶

as shown in the figure. The ray

emerges from the sphere parallel to the line 𝐴𝐴. Find the angle of refraction of 𝐴𝐴 if the
refractive index of material of sphere is √3.
 [CBSE 2014]

3. PRISM AND OPTICAL INSTRUMENTS

Case Based Qs (4 – 5 marks)
43. A number of optical devices and instruments have been designed and developed such as
periscope, binoculars, microscopes and telescopes utilising the reflecting and refracting
properties of mirrors, lenses and prisms. Most of them are in common use. Our knowledge
about the formation of images by the mirrors and lenses is the basic requirement for
understanding the working of these devices.
(A) Why the image formed at infinity is often considered most suitable for viewing?
Explain.

(B) In modern microscopes multi-component lenses are used for both the objective and the
eyepiece. Why?

(C) Write two points of difference between a compound microscope and an astronomical
telescope.

(D) Write two distinct advantages of a reflecting type telescope over a refracting type
telescope.

[CBSE SQP 2022, CBSE 2018]

Very Short & Short Qs (1-3 marks)

44. In an astronomical telescope in normal adjustment a straight black line of length L is
drawn on the objective lens. The eyepiece forms a real image of this line whose length is 𝑙𝑙.
What is the angular magnification of the telescope?
[CBSE SQP 2023]

45. A ray of monochromatic light passes through an equilateral glass prism in such a way that
the angle of incidence is equal to the angle of emergence and each of these angles is 3/4
times the angle of the prism. Determine the angle of deviation and the refractive index of
the glass prism.
[CBSE SQP 2023]
46. A ray of light is incident on a glass prism of refractive index 𝜇𝜇 and refracting angle 𝐴𝐴. If it
just suffers total internal reflection at the other face, obtain a relation between the angle of
incidence, angle of prism and critical angle.
[CBSE 2023]
47. Two prisms 𝐴𝐴𝐴𝐴 and 𝐷𝐷𝐷𝐷 are arranged as shown in figure. The critical angle for the two
prisms with respect to air are 41.1∘ and 45∘ , respectively. Trace the path of the ray
through the combination.

𝐴𝐴

of an isosceles triangular prism makes an angle of

incidence (i) and deviates by angle 𝐵𝐵 as shown in the figure. Show that in the position of
minimum deviation ∠𝛽𝛽 = ∠𝛼𝛼. Also find out the condition when the refracted ray 𝑄𝑄𝑄𝑄
suffers total internal reflection.

[CBSE 2019]

51. (A) When a convex lens of focal length 30 cm is in contact with a concave lens of focal
length 20 cm, find out if the system is converging or diverging.
(B) Obtain the expression for the angle of incidence of a ray of light which is incident on
the face of a prism of refracting angle 𝐴𝐴 so that it suffers total internal reflection at the
other face. (Given the refractive index of the glass of the prism is 𝜇𝜇 ).

[CBSE 2019]
52. How does the angle of minimum deviation of a glass prism vary, if the incident violet light
is replaced by red light? Give reason.
[CBSE 2017]

53. Define the magnifying power of a compound microscope when the final image is formed
at infinity. Why must both the objective and the eyepiece of a compound microscope has
short focal length? Explain.
[CBSE 2017]

54. You are given the following three lenses. Which two lenses will you use as an eyepiece
and as an objective to construct an astronomical telescope? Give reason.

Lenses Power (P) Aperture (A)

L1 3D 8 cm

L2 6D 1 cm

L3 16D 1 cm

𝑄𝑄𝑄𝑄

is parallel to
the base BC, show that

𝐴𝐴
(A) 𝑟𝑟1 = 𝑟𝑟2 = , and
2

(B) Angle of minimum deviation, 𝛿𝛿𝑚𝑚 = 2𝑖𝑖 − A

[CBSE 2014]

56. Draw a schematic diagram of refracting telescope. Write its two important limitations.
[CBSE 2014]

Long Qs

4-5 marks
57. (A) Draw the ray diagram showing the refraction of ray of light through glass prism.
Derive the expression for the refractive index 𝜇𝜇 of the material of prism in terms of the
angle of prism 𝐴𝐴 and angle of minimum deviation 𝛿𝛿𝑚𝑚 .
(B) A ray of light 𝑃𝑃𝑃𝑃 enters an isosceles right angled prism 𝐴𝐴𝐴𝐴 of refractive index 1.5 as
shown in the figure.

𝐴𝐴

of a glass prism 𝐴𝐴𝐴𝐴 of refractive index √3. How will the angle of emergence change
qualitatively, if the ray of light emerges from the prism into a liquid of refractive index 1.3
instead of air?

[CBSE 2020]

59. (A) A ray ' 𝑃𝑃𝑃𝑃 ' of light is incident on the face 𝐴𝐴 of a glass prism 𝐴𝐴𝐴𝐴 (as shown in the
figure) and emerges out of the face 𝐴𝐴. Trace the path of the ray. Show that ∠𝑖𝑖 + ∠𝑒𝑒 =
∠𝐴𝐴 + ∠𝛿𝛿. When 𝛿𝛿 and 𝑒𝑒 denote the angle of deviation and angle of emergence
respectively.
 Plot a graph showing the variation of the angle of deviation as a function of angle of
incidence. State the condition under which ∠𝛿𝛿 is minimum.

(B) Find out the relation between the refractive index (𝜇𝜇) of the glass prism and ∠A for
the case when the angle of prism (𝐴𝐴) is equal to the angle of minimum deviation (𝛿𝛿𝑚𝑚 ).
Hence, obtain the value of the refractive index for angle of prism 𝐴𝐴 = 60∘ .

[CBSE 2015]

Numerical Qs (1-5 marks)

60. A concave mirror of focal length 12 cm forms a three times magnified virtual image of an
object. Find the distance of the object from the mirror.
[CBSE 2023]

61. A ray is incident on a prism of refractive index √2 at point 𝑀𝑀 such that it grazes along NC
after emerging from the prism as shown in the figure. Find

(A) The critical angle of the prism

(B) The angle of refraction at face 𝐴𝐴

[CBSE Term - 2 2022]

62. What is the difference in the construction of an astronomical telescope and a compound
microscope? The focal lengths of the objective and eyepiece of a compound microscope
are 1.25 cm and 5.0 cm, respectively. Find the position of the object relative to the
objective in order to obtain an angular magnification of 30 when the final image is formed
at the near point.
[CBSE 2020, 15]

63. An equilateral glass prism has a refractive index 1.6 in air. Calculate the angle of
4√2
minimum deviation of the prism, when kept in a medium of refractive index .
5

𝐴𝐴

of an equilateral glass prism, shows minimum

deviation of 30∘ . Calculate the speed of light through the prism.
 (B) Find the angle of incidence at face 𝐴𝐴 so that the emergent ray grazes along the face
𝐴𝐴.

[CBSE 2017]

65. A small telescope has an objective lens of focal length 150 cm and eye-piece of focal
length 5 cm. What is the magnifying power of the telescope for viewing distant objects in
normal adjustment?
If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the
image of the tower formed by the objective lens?

[CBSE 2015]

66. (A) A giant refracting telescope has an objective lens of focal length 15 m. If an eye-piece
of focal length 1.0 cm is used. What is the angular magnification of the telescope?
(B) If this telescope is used to view the moon. What is the diameter of the image of the
moon formed by the objective lens? The diameter of the moon is 3.48 × 106 m and the
radius of lunar orbit is 3.8 × 108 m.

[CBSE 2015]

67. 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 eye-piece 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.
[CBSE 2014]

68. 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.
[CBSE 2014]