Suppose light from a 632.8 nm helium-neon laser shines through a diffraction grating ruled at 520 lines/mm. How many bright lines are formed

Question

Suppose light from a 632.8 nm helium-neon laser shines through a diffraction grating ruled at 520 lines/mm. How many bright lines are formed on a screen a distance away?

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Doris 6 months 2021-07-16T11:52:12+00:00 1 Answers 0 views 0

Answers ( )

  1. nguyetanh
    0
    2021-07-16T11:53:47+00:00
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    Answer:

    1 bright fringe every 33 cm.

    Explanation:

    The formula to calculate the position of the m-th order brigh line (constructive interference) produced by diffraction of light through a diffraction grating is:

    y=\frac{m\lambda D}{d}

    where

    m is the order of the maximum

    \lambda is the wavelength of the light

    D is the distance of the screen

    d is the separation between two adjacent slit

    Here we have:

    \lambda=632.8 nm = 632.8\cdot 10^{-9} m is the wavelength of the light

    D = 1 m is the distance of the screen (not given in the problem, so we assume it to be 1 meter)

    n=520 lines/mm is the number of lines per mm, so the spacing between two lines is

    d=\frac{1}{n}=\frac{1}{520}=1.92\cdot 10^{-3} mm = 1.92\cdot 10^{-6} m

    Therefore, substituting m = 1, we find:

    y=\frac{(632.8\cdot 10^{-9})(1)}{1.92\cdot 10^{-6}}=0.330 m

    So, on the distant screen, there is 1 bright fringe every 33 cm.

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