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22 March, 17:46

Light from a sodium lamp passes through a diffraction grating having 1000 slits per millimeter. The interference pattern is viewed on a screen of 1.00m behind the grating. Two bright yellow fringes are visible 72.88cm and 73.00cm from the central maximum.

What are the wavelengths of these two fringes?

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  1. 22 March, 20:42
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    The wavelengths of these two fringes is 589.61 x 10∧9

    Explanation:

    d = slit width = 0.001/1000 = 1 x 10-6 m

    X1 = Position of first fringe = 0.7288 m

    X2 = Position of second fringe = 0.73 m

    D = distance of the screen

    tan/theta1 = X1/D / Rightarrow/theta1 = tan-1 (X1/D) = tan-1 (0.7288/1) = 36.085

    tan/theta2 = X2/D / Rightarrow/theta2 = tan-1 (X2/D) = tan-1 (0.73/1) = 36.129

    position of first bright fringe is given as

    d Sin/theta1 = n/lambda1

    for bright fringe, n = 1

    d Sin/theta1 = / lambda1

    /lambda1 = (1 x 10-6) Sin36.085 = 589 x 10-9

    position of second bright fringe is given as

    d Sin/theta2 = n/lambda2

    for bright fringe, n = 1

    d Sin/theta2 = / lambda2

    /lambda2 = (1 x 10-6) Sin36.129 = 589.61 x 10-9
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