List of Solved Numerical Problems of Unit-9: Physical Optics, HSSC-I (class 11) Physics (Punjab Curriculum Textbook Board, Lahore) With Verified Answers

Numerical Problems 9.1: Light of wavelength 546 nm is allowed to illuminate the slits of Young's experiment. The separation between the slits is 0.10 mm and the distance of the screen form the slits where interference effects are observed is 20 cm. At what angle the first minimum will fall? What will be the linear distance on the screen between adjacent maxima? (Ans: 0.16°, 1.1 mm)

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Numerical Problems 9.2: Calculate the wavelength of light illuminates two, slits 0.5 mm apart and produces an interference pattern on a screen placed 200 cm away from the slits. The first bright fringe is observed at distance of 2.4 mm from the central bright image. (Ans: 600 nm)

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Numerical Problems 9.3: In a double slit experiment the second order maximum occurs at θ = 0.25°. The wavelength is 650 nm. Determine the slit separation. (Ans: 0.3 mm)

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Numerical Problems 9.4: A monochromatic light of wavelength 588 nm is allowed to fall on the half silvered plate G1, in the Michelson interferometer. If mirror M1 is moved through 0.233 mm, how many fringes will be observed to shift? (Ans: 792)

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Numerical Problems 9.5: A second order spectrum is formed at an angle of 38° when light falls normally on a diffraction grating having 5400 lines per centimeter. Determine wavelength of the light used. (Ans: 570 nm)

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Numerical Problems 9.6: A light is incident normally on a grating, which has 2500  lines per centimeter. Compute the enslavement of a spectral line for which the deviation in second order is 15°. (Ans: 518 nm)

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Numerical Problems 9.7: Sodium light of wavelength 589 nm is incident normally on a grating having 3000 lines per centimeter. What is the highest order of the spectrum obtained with this grating? (Ans: 5th)

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Numerical Problems 9.8: Blue light of wavelength 480 nm illuminates a diffraction grating. The second order image is formed at an angle of 30° from the central image. How many lines in a centimeter of the grating have been ruled? (Ans: 5.2ｘ10³ lines per cm)

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Numerical Problems 9.9: X-rays of wavelength 0.15 nm are observed to undergo a first order reflection at a Bragg angle of 13.3° from a quartz (SiO₂) crystal. What is the interplanar spacing of the reflecting planes in the crystal? (Ans: 0.326 nm)

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Numerical Problems 9.10: X-ray beam of wavelength undergoes a first order reflection from a crystal when its angle of incident to a crystal face is 26.5°, and an X-ray beam of wavelength 0.097 nm undergoes a third order reflection when its angle of incidence to that face is 60°. Assuming that the two beams reflect from the same family of planes, calculate (a) the interplanar spacing of the planes and (b) wavelength. (Ans: (a) 0.168 nm, (b) 0.150 nm)

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