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13 September, 17:04

Laser light of wavelength lambda passes through a thin slit of width a and produces its first dark fringes at angles of + / - 30 degree with the original direction of the beam. The slit is then reduced in size to a circle of diameter a. When the same laser light is passed through the circle, the first dark fringe occurs at

A) + / - 66.9 degree.

B) + / - 45.0 degree.

C) + / - 37.6 degree.

D) + / - 36.6 degree.

E) + / - 15.0 degree.

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  1. 13 September, 17:34
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    C - ±37.6°

    Explanation:

    This is the case of a single slit diffraction. In this case, the dark fringe occurs at

    sin θ = ± mλ/a

    where m = 1

    θ = ± 30°

    Hence we have sin ± 30° = ± λ/a

    ±0.5 = ± λ/a

    Hence, we have a = 2λ

    For a circular aperture, the condition for the first dark fringe is

    D = diameter of circle = a = 2λ

    so we have sin θ1 = 1.22λ/a

    sin θ1 = 1.22λ/2λ

    hence sin θ1 = 0.61

    θ1 = sin⁻¹0.61 = ±37.6°
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