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25 June, 23:27

In a Young's double-slit experiment the separation distance y between the second-order bright fringe and the central bright fringe on a flat screen is 0.0199 m, when the light has a wavelength of 425 nm. Assume that the angles are small enough so that sin is approximately equal to tan. Find the separation y when the light has a wavelength of 583 nm.

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  1. 26 June, 02:49
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    separation y when the light has a wavelength of 583 nm is 0.027298 m

    Explanation:

    Given data

    central bright fringe L = 0.0199 m

    m = 2

    wavelength = 425 nm

    to find out

    separation y when the light has a wavelength of 583 nm

    solution

    we have given

    sin (θ) ≅ cos (θ)

    so sin (θ) = mλ / d

    and we say tan (θ) = y/L

    so in small angle we say

    0.0199 / L = 2 (425) / d

    so d/L = 2 (425) / 0.0199 ... a

    and

    now with wavelength 583 nm

    y/L = 2 (583) / d

    d/L = 2 (583) / y ... b

    so from a and b

    2 (583) / y = 2 (425) / 0.0199

    y = 583 (0.0199) / 425

    y = 0.027298 m

    separation y when the light has a wavelength of 583 nm is 0.027298 m
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