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15 February, 14:39

A thin beam of light of wavelength 625 nm goes through a thin slit and falls on a screen 3.00 m past the slit. You observe that the first completely dark fringes occur on the screen at distances of ±8.24 mm from the central bright fringe, and that the central bright fringe has an intensity of 2.00 W/m2 at its center. (a) How wide is the slit?

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  1. 15 February, 17:07
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    a = 2.275 10⁻⁴ m

    Explanation:

    This is a diffraction problem that is described by the equation

    a sin θ = m λ

    The first dark minimum occurs for m = 1

    a = λ / sin θ

    The angle can be found by trigonometry,

    tan θ = y / x

    θ = tan⁻¹ y / x

    Let's reduce the magnitudes to the SI system

    y = 8.24 mm = 8.24 10⁻³ m

    λ = 625 nm = 625 10⁻⁹ m

    θ = tan⁻¹ 8.24 10⁻³ / 3.00

    θ = 0.002747 rad

    We calculate

    a = 625 10⁻⁹ / sin 0.002747

    a = 2.275 10⁻⁴ m
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