Exercises of Wave Optics
1. Choose the correct option
i) Which of the following phenomenon proves that light is a transverse wave?
(A) reflection
(B) interference
(C) diffraction
(D) polarization
ii) Which property of light does not change when it travels from one medium to another?
(A) velocity
(B) wavelength
(C) amplitude
(D) frequency
iii) When unpolarized light is passed through a polarizer, its intensity
(A) increases
(B) decreases
(C) remains unchanged
(D) depends on the orientation of the polarizer
iv) In Young’s double slit experiment, the two coherent sources have different intensities. If the ratio of maximum intensity to the minimum intensity in the interference pattern produced is 25:1. What was the ratio of intensities of the two sources?
(A) 5:1
(B) 25:1
(C) 3:2
(D) 9:4
v) In Young’s double slit experiment, a thin uniform sheet of glass is kept in front of the two slits, parallel to the screen having the slits. The resulting interference pattern will satisfy
(A) The interference pattern will remain unchanged
(B) The fringe width will decrease
(C) The fringe width will increase
(D) The fringes will shift.
2. Answer in brief.
i) What are primary and secondary sources of light?
ii) What is a wavefront? How is it related to rays of light? What is the shape of the wavefront at a point far away from the source of light?
iii) Why are multiple colours observed over a thin film of oil floating on water? Explain with the help of a diagram.
iv) In Young’s double slit experiment what will we observe on the screen when white light is incident on the slits but one slit is covered with a red filter and the other with a violet filter? Give reasons for your answer.
v) Explain what is optical path length. How is it different from actual path length?
3. Derive the laws of reflection of light using Huygens’ principle.
4. Derive the laws of refraction of light using Huygens’ principle.
5. Explain what is meant by polarization and derive Malus’ law.
6. What is Brewster’s law? Derive the formula for Brewster angle.
7. Describe Young’s double slit interference experiment and derive conditions for occurrence of dark and bright fringes on the screen. Define fringe width and derive a formula for it.
8. What are the conditions for obtaining good interference pattern? Give reasons.
9. What is meant by coherent sources? What are the two methods for obtaining coherent sources in the laboratory?
10. What is diffraction of light? How does it differ from interference? What are Fraunhoffer and Fresnel diffractions?
11. Derive the conditions for bright and dark fringes produced due to diffraction by a single slit.
12. Describe what is Rayleigh’s criterion for resolution. Explain it for a telescope and a microscope.
13. White light consists of wavelengths from 400 nm to 700 nm. What will be the wavelength range seen when white light is passed through glass of refractive index 1.55?[Ans: 258.06 – 451.61 nm]
14. The optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is same as that on travelling a distance x cm through a medium having refractive index 1.25. Determine the value of x.
[Ans: 3.84 cm]
15. A double-slit arrangement produces interference fringes for sodium light (λ = 589 nm) that are 0.20° apart. What is the angular fringe separation if the entire arrangement is immersed in water (n = 1.33)?
[Ans: 0.15°]
16. In a double-slit arrangement the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits. (a) What is the angular separation in radians between the central maximum and an adjacent maximum? (b) What is the distance between these maxima on a screen 50.0 cm from the slits?
[Ans: 0.01 rad, 0.5 cm]
17. Unpolarized light with intensity Io is incident on two polaroids. The axis of the first polaroid makes an angle of 50° with the vertical, and the axis of the second polaroid is horizontal. What is the intensity of the light after it has passed through the second polaroid?
[Ans: Io ⁄ 2 x (cos 400)2]
18. In a biprism experiment, the fringes are observed in the focal plane of the eyepiece at a distance of 1.2 m from the The distance between the central bright band and the 20th bright band is 0.4 cm. When a convex lens is placed between the biprism and the eyepiece, 90 cm from the eyepiece, the distance between the two virtual magnified images is found to be 0.9 cm. Determine the wavelength of light used.
[Ans: 5000 A]
19. In Fraunhoffer diffraction by a narrow slit, a screen is placed at a distance of 2m from the lens to obtain the diffraction pattern. If the slit width is 0.2 mm and the first minimum is 5 mm on either side of the central maximum, find the wavelength of light.[Ans: 5000 A]
20. The intensity of the light coming from one of the slits in Young’s experiment is twice the intensity of the light coming from the other slit. What will be the approximate ratio of the intensities of the bright and dark fringes in the resulting interference pattern? [Ans: 34]
21. A parallel beam of green light of wavelength 546 nm passes through a slit of width 0.4 mm. The intensity pattern of the transmitted light is seen on a screen which is 40 cm away. What is the distance between the two first order minima?
[Ans: 1.1 mm]
22. What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at 45.0°?
[Ans: 1.27]
23. Monochromatic electromagnetic radiation from a distant source passes through a slit. The diffraction pattern is observed on a screen 2.50 m from the If the width of the central maximum is 6.00 mm, what is the slit width if the wavelength is (a) 500 nm (visible light); (b) 50 pm (infrared radiation); (c) 0.500 nm (X-rays)?
[Ans: 0.416 mm, 41.6 mm, 4.16×10-4 mm]
24. A star is emitting light at the wavelength of 5000 Å. Determine the limit of resolution of a telescope having an objective of diameter of 200 inch.
[Ans: 1.2×10-7 rad]
25. The distance between two consecutive bright fringes in a biprism experiment using light of wavelength 6000 Å is 32 mm by how much will the distance change if light of wavelength 4800 Å is used?
[Ans: 0.064 mm]