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24 November, 08:20

Light of wavelength 600nm illuminates a diffraction grating. The second-order maximum is at angle 39°. How many lines per millimeter does this grating have?

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  1. 24 November, 08:36
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    the number of lines is 526

    Explanation:

    The wavelength λ = 600nm = 600 * 10⁻⁶ mm

    The diffraction angle θ = 39°

    Recall the expression for the relation between the wavelength, angle and central maxima distance.

    Recall the expression for the relation between the wavelength, angle and central maxima distance.

    Recall the expression for the relation between the wavelength, angle and central maxima distance.

    relation between the wave length, angle and central maxima distance

    d = nλ / sinθ

    Here n = 2 for second order maxima and d is the distance

    = 2 (600 * 10⁻⁶) / sin 39°

    = 1200 * 10⁻⁶ / 0.6293

    = 1.9 * 10⁻³ mm

    N = 1/d

    = 1 / 1.9 * 10⁻³

    = 526

    The grating has a line density of 526 lines per millimeter
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