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31 October, 01:52

A lab technician uses laser light with a wavelength of 670 nm to test a diffraction grating. When the grating is 40.0 cm from the screen, the first-order maxima appear 6.00 cm from the center of the pattern. How many lines per millimeter does this grating have?

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  1. 31 October, 02:14
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    N = 221.4 lines / mm

    Explanation:

    Given:

    - The wavelength of the source λ = 670 nm

    - Distance of the grating from screen B = 40.0 cm

    - The distance of first bright fringe from central order P = 6.0 cm

    Find:

    How many lines per millimeter does this grating have?

    Solution:

    - The derived results from Young's experiment that relates the order of bright fringes about the central order is given by:

    sin (Q) = n*λ*N

    Where,

    n is the order number 0, 1, 2, 3, ...

    λ is the wavelength of the light source

    Q is the angle of sweep respective fringe from central order

    N is the number of lines/mm the grating has

    - We will first compute the length along which the light travels for the first bright fringe:

    L^2 = P^2 + B^2

    L^2 = 40^2 + 6^2

    L^2 = 1636

    L = 40.45 cm

    - Now calculate the sin (Q) that the fringe makes with the central order:

    sin (Q) = P / L

    sin (Q) = 6 / 40.45

    - Now we will use the derived results:

    N = sin (Q) / n*λ

    Where, n = 1 - First order

    Plug values in N = (6 / 40.45) / (670 * 10^-6)

    N = 221.4 lines / mm
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