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Refraction of Light â?– Illustrative Examples 1) A ray of light is incident on the surface of water at an angle of incidence of 70o. The ray is deviated through 25o towards the normal when it enters the water. Calculate the refractive index of water. Data :
(Ans. :
)
2) Calculate the speed of light in a medium whose critical angle is 49o.
Data :
(Ans. :
)
3) A ray of light incident at an angle of 50o on one face of an equilateral prism gets deviated through 37o, find its angle of emergence. Data :
(Ans. :
)
4) Calculate the angle of minimum deviation of a ray of light passing through an equilateral prism of refractive index 1.62. Data :
(Ans. :
)
5) The refractive indices of the material of a prism for red and violet colours are 1.72 and 1 .75 respectively. Determine the angular dispersion and dispersive power, if refracting angle of prism is 6o.
Data :
(Ans. :
)
6) For certain prism, the angle of minimum deviation is equal to the refracting angle of prism. The refractive index of the material of the prism is 1.7. Find i) the angle of minimum deviation, ii) the angle of incidence when the minimum deviation takes place. Data : 7) Wavelengths of light in water and glass are 4000
(Ans. : and 2500
)
respectively. Find
the refractive index of glass with respect to water. Data :
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(Ans. :
Refraction of Light
)
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8) The minimum deviation produced by an equilateral glass prism is 30o. If the velocity of light in vacuum is 3 × 108m/s., calculate the velocity of light in glass. Data :
(Ans. :
)
9) A glass prism has minimum angle of deviation 40o. Refracting angle of prism is 60o. The prism is placed in water of R.I. 1.33. What will be the new minimum angle of deviation? Data : 10)
(Ans. :
)
For a certain prism it is found that the angle of deviation is 40o for two values of angle of incidence 52o and 48o. Determine the refracting angle of the prism. Data :
(Ans. :
)
❖ Theory Question 1)
State the Snell’s laws of refraction of light.
2)
State i) Snell’s law, ii) the principle of reversibility of light.
3)
With the help of a neat ray diagram, explain the phenomenon of total internal reflection.
4)
State at least three applications of total internal reflection.
5)
Explain the critical angle with the help of diagram.
6)
Discuss the construction, working and uses of the optical fibres.
7)
What is dispersion of light?
8)
For a prism, prove the relation
where the symbols have their usual
meanings. 9)
With the help of a, neat ray diagram, obtain an expression for the refractive index of material of a prism.
10)
Derive an expression for the deviation clue to a thin prism.
11)
Define (a) angular dispersion (b) dispersive power of a prism and derive their expressions.
12)
Explain (a) deviation without dispersion and (b) dispersion without deviation.
13)
What is a rainbow? How is it formed?
14)
Why does the sequence of colours in the secondary rainbow is opposite to that in the primary rainbow?
15)
Write a short note on scattering of light.
16)
Why does the sky appear blue during the day'?
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Refraction of Light
INFOMATICA ACADEMY 17)
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Explain why the sun appears orange-reddish in colour just before sunset and just after sunrise.
18)
Define monochromatic light?
19)
Define the following terms. i. Partial reflection ii. Refraction of light
20)
Define the following terms. i. Angle of incidence ii. Angle of refraction
21)
Define the following terms. i. Glancing angle ii. Angle of deviation
22)
Define the following terms. i. Relative refractive index ii. Absolute refractive index
23)
Draw a neat labelled diagram to show laws of refraction.
24)
Explain the phenomenon of refraction with suitable examples.
25)
Show that
26)
Figures (a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass- air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence in water is 45° with the normal to a water-glass interface [Figure (c)].
27)
Define relative refractive index in terms of wavelength and hence show that
28)
State the main applications of refraction of light in daily life.
29)
A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
30)
A lemon is kept in water in a glass beaker and viewed from the sides. Does it look bigger or smaller than its actual size? Why?
31)
State the necessary condition for total internal reflection.
32)
Explain the application of total internal reflection in reflecting prisms.
33)
Give reason for sparkling of a diamond.
34)
Define mirage. Explain occurrence of mirage in our daily life.
35)
Give a note on spectrum?
36)
Define prism.
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Explain/Define the following terms in a prism. i. Refracting angle ii. Refracting surfaces iii. Refracting edge iv. Principal section v. Base of the prism 37)
Define the following terms. i. Angle of deviation ii. Angle of minimum deviation iii. Angle of emergence
38)
Explain
versus i curve for refraction of light through a prism.
39)
A glass prism is dipped in water. Will its dispersive power change?
40)
Define primary rainbow and secondary rainbow.
41)
Explain the formation of primary and secondary rainbow in the sky.
42)
Explain the characteristics of primary rainbow.
43)
Explain the characteristics of secondary rainbow.
44)
Rainbows are seen in the afternoon. Is it possible to view rainbow in the morning?
45)
Why is the appearance of sky in large industrial cities different from the villages?
46)
State and explain Rayleigh’s law of scattering.
47)
Explain various applications of scattering of light in our daily life.
48)
State Raman effect.
49)
State the applications of Raman effect.
❖ Textbook Problems 1)
Find the critical angle for a ray of light at glass - water interface if refractive indices for glass and water are 1.62 and 1.32 respectively.
2)
(Ans : 1.333)
A ray of light is incident at an angle of 50o with the surface of glass of refractive index 1.5. Find the deviation of ray when it enters glass.
5)
(Ans : 7.5m)
Find the refractive index of water given that the velocities of light in air and water are respectively 3 × 108 m/s and 2.25 × 108 m/s
4)
)
The depth of a pond is 10 m. What is the apparent depth for a person looking normally to the water surface?
3)
(Ans :
(Ans :
)
A thin prism of 3o angle gives a deviation of 1.6o. What is the refractive index of the material of prism?
F.Y.J.C.
(Ans : 1.533) Refraction of Light
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The refractive indices of the material of the prism for red and yellow colour are 1.620 and 1.635 respectively. Calculate the angular dispersion and dispersive power, if refracting angle is 8o.
7)
A light of wavelength 6000
(Ans : 0.24o, 0.0472)
in air, enters a medium of refractive index 1.5. What
will be the frequency and wavelength of light in the medium? (Ans : 5 × 1014 Hz, 4ooo 8)
A thin hollow prism of refracting angle 3o, filled with water gives a deviation of 1o. What is the refractive index of water?
9)
)
(Ans : 1.333)
A thin prism produces an angular dispersion of
. If the refracting angle of prism
is 2o and the R.I. of its material for violet light is 1.74. calculate the R.I. of its material for red light. 10)
(Ans : 1.59)
In an equilateral glass prism, for two angles of incidence, differing by 10o, the angle of deviation is found to be 40o, find these angles of incidence. (Ans : 55o and 45o)
❖ Practise Problems ➢ Type-I : Problems based on Snell’s law 1) A ray of light is incident on a glass plate making an angle of 60° with the normal at the point of incidence. If the reflected and refracted rays are perpendicular, find the refractive index (R.I.) of glass.
(Ans : 1.732)
2) The refractive index of water relative to air is 4/3. A ray of light passing from water into air is incident at the interface at an angle of 35° to the normal. What angle does the refracted ray make with the normal ?
(Ans : 49°.54')
3) A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again? 4) A ray of light falls on a glass plate perpendicular, find the angle of incidence.
(Ans : 1.7 cm) If the reflected and refracted rays are (Ans : 58o 18’)
5) Find the angle at which a ray of light must be incident on the face of an equilateral prism so that it just suffers total internal reflection at the other refracting face. [
for glass of which the prism is made = 1.5].
F.Y.J.C.
(Ans : 28°)
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6) A ray of light is incident from a rarer medium (
= 1.5) into a denser medium. If the
angle of incidence and refraction are respectively 60° and 45°, calculate the refractive index of the denser medium.
(Ans : 1.83)
7) A ray of light is incident on the surface of a liquid from air at 60°. If after refraction it bends towards the normal through 45°, then calculate the R.I. of liquid. (Ans : 1.22) 8) A vessel of water is 2 metre deep. How deep will it appear if looked vertically downward ?
(Ans : 1.5 m)
9) Rays from a point source of light situated below the water surface, form a circular patch of light of radius 30 cm on the surface. At what depth is the light source situated? [ 10)
for water = 1.33]
(Ans : 26.3 cm)
A ray of light is incident on a glass slab making an angle of 60° with the surface. Calculate the angle of refraction in glass and the velocity of light in glass if the refractive index of glass and the velocity of light in air are 1.5 and 3 × 108 m/s respectively.
11)
(Ans :
)
What is the change in the wavelength of monochromatic light ray when it passes from air to a medium of refractive index 1.6? [Frequency of light
Hz] (Ans :
)
➢ Type-II : Problems based on critical angle 12)
A ray of light passes from glass
to water
angle of incidence? 13)
Calculate the critical angle between glass and air.
14)
Find the critical angle between water and glycerine, [ glycerine = 1.47]
15)
What is the critical (Ans : 61°.2') (Ans : 41o 48’) for water = 1.33 and for (Ans : 64o 48’)
A ray of light with angle of incidence 45° is refracted through prism of refracting angle 60° and suffers minimum deviation. Calculate the R.I. of the material of prism.
F.Y.J.C.
(Ans : 1.414)
Refraction of Light
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A ray of light is incident normally on one of the refracting faces of a prism of refracting angle of 40°. If the emergent ray grazes the second refracting surface, find the R.I. of the material of the prism.
17)
(Ans : 1.56)
The critical angle for a ray is 38°42' for glass and 42° for glycerine. What is the R.I. of glycerine with respect to glass?
(Ans : 0.2)
➢ Types-III : Problems based on prism formula 18)
A prism has a refractive index 1.427. For a certain ray of light, it produces a deviation of 32° 40'. Find the angle of the prism.
19)
(Ans : 62°.)
A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be 40°. What is the refractive index of the material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light. (Ans : (i) 1.5321 (ii) = 10°20')
20)
At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.
21)
(Ans : 10°)
A monochromatic beam of light strikes the surface of a lake at an angle of incidence of 30°. Find the angle through which the beam is deviated when it enters water.
22)
(Ans : 7°55')
When the angle of incident on a refracting face of a glass prism is 45°, the angle of emergence at the other face is found to be 54° 16'. Find the refracting angle of the prism.
23)
(Ans : 56°18')
A ray of light incident normally on one of the refracting faces of the prism suffers a deviation of 30°. If the emergent ray is parallel to the second refracting face, find the angle of the prism.
24)
Calculate the refractive index of the material of an equilateral prism for which the angle of minimum deviation is 60°.
25)
(Ans : 60°) (Ans : 1.73)
A glass prism of certain material produces a minimum deviation of 16° when its refracting angle is 30°. What will be the angle of minimum deviation produced by a prism of the same material having refracting angle of 60°?
(Ans : 38°)
➢ Type-IV : Problems based on angular dispersion and dispersive Power
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Refraction of Light
INFOMATICA ACADEMY 26)
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A thin prism produces deviations of 5.04°, 5.31° and 5.63° respectively for red, yellow and violet colours. Find the dispersive power of the prism.
27)
(Ans: 0.1111)
A prism with refracting angle of 60°, gives angle of minimum deviation 53°, 51° and 52° for blue, red and yellow light respectively. What is the dispersive power of the material of the prism ?
28)
(Ans : 0.038)
A glass prism deviates the red and the blue rays through 10° and 12° respectively. A second prism of equal angle deviates then through 8° and 10° respectively. Find the ratio of their dispersive powers.
29)
(Ans : 9 : 11)
A thin prism of 6° angle gives a minimum deviation of 3°. What is the refractive index of the material of the prism ?
(Ans : 1.5)
➢ Type-V : Miscellaneous 30)
Monochromatic light of wavelength 480 nm travelling in air is incident on a glass surface. Find the wavelength, frequency and the velocity of light in glass, [ for glass,
31)
]
(Ans :
)
If the refractive indices of glycerine and diamond with respect to air are 1.4 and 2.4 respectively, calculate the speed of light in glycerine and in diamond. From these results, calculate the R.I. of diamond with respect to glycerine. (Ans :
32)
)
A thin glass prism has refracting angle of 5°. The R.I. of glass for violet and red colours are 1.61 and 1.59 respectively. Find the angular dispersion produced by the prism and dispersive power of the material of prism.
(Ans : 0.1°, 0.033)
❖ Multiple Choice Questions 1) If the speed of red light is denoted by vr and the speed of violet light vv, then for vacuum (A)
(B)
(C)
(D)
2) For a wave propagating in a medium, identify the property which is independent of others. (A) refractive index
(C) velocity of source
(B) amplitude of waves
(D) frequency
3) Time taken by light to cross a glass slab of thickness 4 mm and refractive index 3 is (A)
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(B)
(C)
(D)
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4) Light travels from a medium of refractive index
to another of refractive index
For total internal reflection of light, which is NOT true? (A) Light must travel from medium of refractive index
.
(B) Angle of incidence must be greater than the critical angle. (C) There is no refraction of light. (D) Light must travel from the medium of refractive index
.
5) When light rays travel from air to water separated by sharp boundary, (A) it proceeds undeviated.
(C) it bends away from the normal.
(B) it bends towards the normal.
(D) it is reflected
6) When a ray of light enters a glass slab from air (A) its wavelength decreases.
(C) its frequency increases
(B) its wavelength increases.
(D) neither wavelength nor frequency changes
7) One cannot see through fog because (A) fog absorbs light. (B) the refractive index of fog is infinity. (C) light suffers total reflection at the droplet in a fog. (D) light is scattered by the droplets in fog. 8) A monochromatic beam of light passes from a denser medium to a rarer medium. As a result (A) its velocity increases.
(C) its frequency decreases.
(B) its velocity decreases.
(D) its wavelength decreases.
9) A completely transparent material will be invisible in vacuum when its refractive index is _______. (A) unity
(C) less then unity
(B) more than unity
(D) equal to 1.33
10) Critical angle of light passing from glass to air is minimum for ______. (A) red
(B)green
(C) yellow
(D) violet
11) To an observer on the earth, the stars appear to twinkle. This can be ascribed to (A) the fact that stars do not emit light continuously. (B) frequency absorption of star light by their own atmosphere. (C) frequency absorption of star light by the earth’s atmosphere. (D) the refractive index fluctuations in the earth’s atmosphere.
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12) A glass slab is placed in the path of a beam of convergent light. The point of convergence of light (A) moves towards the glass slab. (B) moves away from the glass slab. (C) remains at the same point. (D) undergoes a lateral shift. 13) A ray of light travelling inside a rectangular glass block of refractive index
is
incident on the glass-air surface at an angle of incidence of 45°. The refractive index of air is one. Under these conditions, the ray (A) will emerge into the air without any deviation. (B) will be reflected back into the glass. (C) will be absorbed. (D) will emerge into the air with an angle of refraction equal to 90°. 14) Mirages are observed in deserts due to the phenomenon of _______. (A) interference of light (B)total reflection of light
(C) scattering of light (D) double refraction of light
15) The refractive index of glass is 1.5, the velocity of light in glass is ________. (A)
(B)
(C)
(D) 1010cm/S
16) The velocity of light in glass whose refractive index with respect to air is 1.5 is In a certain liquid, the velocity of light is found to be
The refractive index of
the liquid with respect to air is (A) 0.64
(B) 0.80
(C) 1.20
(D) 1.44
17) If the refractive index of water is 4/3 and that of glass slab is 5/3. Then the critical angle of incidence for which a light ray tending to go from glass to water is totally reflected, is (A)
(B)
(C)
(D)
18) A ray of light passes from vacuum into a medium of refractive index
, the angle of
incidence is found to be twice the angle of refraction. Then the angle of incidence is (A)
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(B)
(C)
(D)
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19) The critical angle for a medium is 60°. Then the refractive index of the medium will be (A)
(B)
(C)
(D)
20) Rays of light fall on a glass plate, the refractive index of which is p. If the angle between the reflected and refracted rays is 90°, then the angle of incidence is
(A)
(B)
(C)
(D)
21) If the critical angle for the material of a prism is C and the angle of the prism is A, then there will be no emergent ray when (A) 22)
(B)
(C)
(D)
A beam of monochromatic blue light having wavelength 4200 A in air travels in water Its wavelength in water will be (A)
(B)
(C)
(D)
23) If the refractive indices of crown glass for red, yellow and violet colours are 1.5140, 1.5170 and 1.5318 respectively and for flint glass these are 1.6434, 1.6499 and 1.6852 respectively, then the dispersive power for crown and flint glass are respectively (A) 0.034 and 0.064
(C) 1.3 and 0.064
(B) 0.064 and 0.034
(D) 0.034 and 1.0
24) A ray of light is incident at an angle of 60° on one face of a prism of angle 30°. The emergent ray of light makes an angle of 30° with incident ray. The angle made by emergent ray with second face of prism will be (A) 0°
(B) 90°
(C) 45°
(D) 30°
25) The sun is visible before the sunrise and after the sunset because of the phenomenon of _______. (A) reflection
(B)refraction
(C) dispersion
(D) polarization
26) Optical fibre is based on which of the following phenomenon? (A) Reflection.
(C) Total internal reflection.
(B) Refraction.
(D) Dispersion.
27) The phenomenon of total internal reflection takes place only when (A) light travels from denser to rarer medium at any angle of incidence. (B) light travels from denser to rarer medium at an angle of incidence equal to critical angle.
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(C) light travels from rarer medium to denser medium at an angle of incidence greater than the critical angle. (D) light travels from denser to rarer medium at an angle of incidence greater than the critical angle. 28) A thin prism of angle 2° deviates a ray of light through 1° while passing through it. The refractive index of the material of prism is (A) 1.1
(B) 1.15
(C) 1.33
(D) 1.50
29) A blue glass plate is kept below sodium lamp, its colour will be ________. (A) white
(B) yellow
(C) blue
(D) black
30) When a glass rod is immersed in a liquid of same refractive index, it will _______. (A) appear bent
(C) appear longer
(B) disappear
(D) not be affected
31) For prism in minimum deviation position, which of the following statement is correct? (A) Angle of incidence is equal to angle of emergence. (B) Angle of incidence is equal to angle of deviation. (C) Angle of incidence is equal to angle of refraction. (D) Angle of incidence is equal to angle of prism. 32) The critical angle of light passing from glass to air is maximum for _______. (A) red
(B)orange
(C) yellow
(D) violet
33) While deriving prism formula, which of the following condition is NOT satisfied? (A)
(B)
(C)
(D)
34) A beam of monochromatic light is refracted from vacuum into a medium of refractive index 1.5. The wavelength of refracted light will be _______. (A) Same
(C) larger
(B) dependent on intensity of refracted light
(D) smaller
35) For a ray of light passing through prism, which of the following statements is true in case of ‘i’ and ‘ ’? (A) As ‘i’ increases ‘ ’ decreases continuously. (B) As ‘i’ increases ‘ ’ increases continuously. (C) As ‘i’ increases ‘ ’ decreases, reaches minimum value and again it increases. (D) As ‘i’ increases ‘ ’ increases, reaches maximum value and again it decreases.
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36) A ray of light enters from denser medium into rarer medium. The speed of light in rarer medium is twice that in denser medium. The critical angle for this pair of media is (A) 30°
(B) 45°
37) A light of wavelength 5100
(C) 60°
(D) 120°
in air enters a medium of refractive index 1.5, the
wavelength of light in that medium is (A)
(B)
(C)
(D)
38) A bucket completely full of water is 46 cm deep. A coin kept at the bucket when viewed normally will appear at (A) 40 cm
(B) 34.5 cm
(C) 39 cm
(D) 32 cm
39) The rectangular tank 6 m deep is full of water. If the refractive index of water is 1.33, the bottom appears to be raised when viewed normally, to (A) 1.33 m
(B)1.49 m
(C) 4.02 m
(D) 4.51m
40) When a beam of monochromatic light passes through an organic medium, then it is found to contain different frequencies. This phenomenon is known as ______. (A) Raman effect
(C) Polarization
(B) Dispersion
(D) Total internal reflection
❖ Answer to Multiple Choice Question 1. (B)
2. (D)
3. (A)
4. (D)
5. (B)
6. (A)
7. (D)
8. (A)
9. (A)
10. (D)
11. (D)
12. (A)
13. (D)
14. (B)
15. (C)
16. (C)
17. (D)
18. (B)
19. (B)
20. (C)
21. (C)
22. (C)
23. (A)
24. (B)
25. (B)
26. (C)
27. (D)
28. (D)
29. (D)
30. (B)
31. (A)
32. (A)
33. (D)
34. (D)
35. (C)
36. (A)
37. (C)
38. (B)
39. (D)
40. (A)
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