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Physical Optics, Numerical Problems

See here solved numerical problems on Physical Optics included in the course of First Year Physics.

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Problem 1 In a Young’s double slit experiment, the separation of the slits is 1 mm and red light of wavelength 620 nm is falling on it. Determine the distance between the central bight band and the fifth bright fringe on the screen which is 3 m away from the slit.
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Problm 2 Two parallel slits are illuminated by two wavelengths one of which is 5.8 × 10-7 m. On the screen the fourth dark line of the known wavelength coincides with the fifth bright line of the light of the unknown wavelength. Find the unknown wavelength.
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Problem 3 When the movable mirror of the Michelson interferometer is moved 0.1 mm. How many dark fringes pass the reference point if light of wavelength 580 nm is used?
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Problem 4 A soap film has a refractive index of 1.40. How thick must the film be, if it appears black when mercury light of wavelength 546.1 nm falls on it normally?
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Problem 5 A diffraction grating has 5000 lines per centimeter. At what angle does the second order spectrum of the sodium yellow light of wavelength 589 nm occur?
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Problem 6 Light is incident normally on a grating which has 250 lines/mm. Find the wavelength of the spectral line for which the deviation in second order is 12o.
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Problem 7 In a certain X-rays diffraction experiment, the first order fringe is observed at an angle of 5o for a crystal plane spacing of 2.8 × 10-10 m. What is the wavelength of X ray used?
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Problem 8 An X-ray beam of wavelength 0.48 × 10-10 is used to get Brag reflection from a crystal at an angle of 20o for the first order maxima. What are the possible layer spacing which gives rise to this maxima?
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Problem 9 The spacing of one set of crystal planes in NaCl (table salt) is d = 0.282 nm. A monochromatic beam of X-rays produces a Bragg maximum when its glancing angle with these planes is θ = 7°. Assuming that this is a first order maximum (n = 1) find the wave length of the X-rays.
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