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17 April, 22:08

If white light illuminates a diffraction grating having 790 lines/mm, over what range of angles does the visible m = 1 spectrum extend?

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  1. 17 April, 22:32
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    We are given the property of the illuminating light:

    790 lines/mm

    Which is also equivalent to:

    790,000 lines/m

    Taking the reciprocal of this value will give us the distance per line:

    d = 1 m / 790,000 lines

    d = 1.2658 * 10^-6 m

    Now we can solve for the range of angles using the formula

    λ = d * sin θ

    sin θ = λ / d

    where λ is the wavelength of light and θ is the angle

    Now we know that visible light ranges from 400 to 700 nm, therefore we use these values to find the range.

    when λ = 400 nm = 400 * 10^-9 m

    sin θ = 400 * 10^-9 m / 1.2658 * 10^-6 m

    θ = 18.42°

    when λ = 700 nm = 700 * 10^-9 m

    sin θ = 700 * 10^-9 m / 1.2658 * 10^-6 m

    θ = 33.57°

    Therefore the range of angles is 18.42 ° to 33.57 °.
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