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31 December, 00:30

Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.86 m away. If the first-order maxima are separated by 1.42 m on the screen, what is the distance between the two second-order maxima?

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  1. 31 December, 00:56
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    the distance between the two second-order maxima = 3.784m

    Explanation:

    distance between the slit and the screen L = 1.86 m

    first order maxima are separed by x = 1.42 m / 2

    = 0.71m

    x = L tanθ₁

    θ₁ = tan⁻¹ (x / L)

    = tan⁻¹ (0.71 / 1.86)

    = 20.89°

    diffraction d sinθ = mλ

    first order maxima m = 1

    sinθ₁ = λ / d

    λ / d = sin20.89°

    =0.3566

    Second order maxima

    sinθ₂ = 2 (λ / d)

    sinθ₂ = 2 (0.3566)

    = 0.7132

    θ₂ = sin⁻¹ 45.49°

    distance between the second order maxima

    2x = 2 L tanθ₂

    = 2 (1.86) tan45.49°

    = 3.784m
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