Physics · Textbook solutions

Wave Optics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 41 questions

7. Wave Optics — worked examples

8 q

Solved Examples

Worked · 8
  1. Solved Ex.7.1
    Unpolarized light of intensity I0I_0 is made to pass through three polarizers P1P_1, P2P_2 and P3P_3 successively. The polarization axis of P2P_2 makes an angle of θ1\theta_1 with that of P1P_1, while that of P3P_3 makes an angle θ2\theta_2 with that of the P2P_2. What will be the intensity of light coming out of P3P_3?
  2. Solved Ex.7.2
    For what angle of incidence will light incident on a bucket filled with liquid having refractive index 1.5 be completely polarized after reflection?
  3. Solved Ex.7.3
    Plane wavefront of light of wavelength 5500 Å is incident on two slits in a screen perpendicular to the direction of light rays. If the total separation of 10 bright fringes on a screen 2 m away is 2 cm, find the distance between the slits.
  4. Solved Ex.7.4
    In a Young's double slit experiment, the difference in path lengths between the rays starting from the two slits S1S_1 and S2S_2 and reaching a point A on the screen is 0.0075 mm and reaching another point B on the screen on the other side of the central fringe is 0.0015 mm. How many bright and dark fringes are observed between A and B if the wavelength of light used is 6000 Å?
  5. Solved Ex.7.5
    An isosceles prism of refracting angle 179∘179^\circ and refractive index 1.5 is used as a biprism by keeping it 10 cm away from a slit, the edge of the biprism being parallel to the slit. The slit is illuminated by a light of wavelength 500 nm and the screen is 90 cm away from the biprism. Calculate the location of the centre of 20th20^{\text{th}} dark band and the path difference at this location.
  6. Solved Ex.7.6
    What must be the thickness of a thin film which, when kept near one of the slits shifts the central fringe by 5 mm for incident light of wavelength 5400 Å in Young's double slit interference experiment? The refractive index of the material of the film is 1.1 and the fringe width is 0.5 mm.
  7. Solved Ex.7.7
    A telescope has an objective of diameter 2.5 m. What is its angular resolution when it observes at 5500 Å?
  8. Solved Ex.7.8
    What is the minimum distance between two objects which can be resolved by a microscope having the visual angle of 30∘30^\circ when light of wavelength 500 nm is used?

Exercises

33 q

Choose the correct option

Practice · 5
  1. Choose the correct option.
    Ex Q.1 (i)
    Which of the following phenomenon proves that light is a transverse wave?
    1. A.
      reflection
    2. B.
      interference
    3. C.
      diffraction
    4. D.
      polarization
  2. Ex Q.1 (ii)
    Which property of light does not change when it travels from one medium to another?
    1. A.
      velocity
    2. B.
      wavelength
    3. C.
      amplitude
    4. D.
      frequency
  3. Ex Q.1 (iii)
    When unpolarized light is passed through a polarizer, its intensity
    1. A.
      increases
    2. B.
      decreases
    3. C.
      remains unchanged
    4. D.
      depends on the orientation of the polarizer
  4. Ex Q.1 (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?
    1. A.
      5:1
    2. B.
      25:1
    3. C.
      3:2
    4. D.
      9:4
  5. Ex Q.1 (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
    1. A.
      The interference pattern will remain unchanged
    2. B.
      The fringe width will decrease
    3. C.
      The fringe width will increase
    4. D.
      The fringes will shift.

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (i)
    What are primary and secondary sources of light?
  2. Ex Q.2 (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?
  3. Ex Q.2 (iii)
    Why are multiple colours observed over a thin film of oil floating on water? Explain with the help of a diagram.
  4. Ex Q.2 (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.
  5. Ex Q.2 (v)
    Explain what is optical path length. How is it different from actual path length?

Solve the following

Practice · 23
  1. Ex Q.3
    Derive the laws of reflection of light using Huygens' principle.
  2. Ex Q.4
    Derive the laws of refraction of light using Huygens' principle.
  3. Ex Q.5
    Explain what is meant by polarization and derive Malus' law.
  4. Ex Q.6
    What is Brewster's law? Derive the formula for Brewster angle.
  5. Ex Q.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.
  6. Ex Q.8
    What are the conditions for obtaining good interference pattern? Give reasons.
  7. Ex Q.9
    What is meant by coherent sources? What are the two methods for obtaining coherent sources in the laboratory?
  8. Ex Q.10
    What is diffraction of light? How does it differ from interference? What are Fraunhoffer and Fresnel diffractions?
  9. Ex Q.11
    Derive the conditions for bright and dark fringes produced due to diffraction by a single slit.
  10. Ex Q.12
    Describe what is Rayleigh's criterion for resolution. Explain it for a telescope and a microscope.
  11. Ex Q.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?
  12. Ex Q.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 xx cm through a medium having refractive index 1.25. Determine the value of xx.
  13. Ex Q.15
    A double-slit arrangement produces interference fringes for sodium light (λ=589(\lambda = 589 nm)) that are 0.20∘0.20^\circ apart. What is the angular fringe separation if the entire arrangement is immersed in water (n=1.33)(n = 1.33)?
  14. Ex Q.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?
  15. Ex Q.17
    Unpolarized light with intensity I0I_0 is incident on two polaroids. The axis of the first polaroid makes an angle of 50∘50^\circ 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?
  16. Ex Q.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 slits. The distance between the central bright band and the 20th20^{\text{th}} 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.
  17. Ex Q.19
    In Fraunhoffer diffraction by a narrow slit, a screen is placed at a distance of 2 m 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.
  18. Ex Q.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?
  19. Ex Q.21
    A parallel beam of green light of wavelength 550 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?
  20. Ex Q.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∘45.0^\circ?
  21. Ex Q.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 slit. 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 μ50\ \mum (infrared radiation); (c) 0.500 nm (X-rays)?
  22. Ex Q.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.
  23. Ex Q.25
    The distance between two consecutive bright fringes in a biprism experiment using light of wavelength 6000 Å is 0.32 mm by how much will the distance change if light of wavelength 4800 Å is used?