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15 January, 13:17

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.01 mm apart and position your screen 3.65 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 641 nm. How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in millimeters.

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  1. 15 January, 13:46
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    2.316e-3 and 3.47e-3

    Explanation:

    Now, at that angle, we look at the bright spots on the screen.

    tan θ = x / L (x is the horizontal distance from the centre of the screen, L is distance to screen)

    For small angles, we can approximate that tan θ = sin θ.

    nλ / d = x / L so then x = n λ L / d

    First bright fringe, n = 1

    x = (1) (641*10^-9 m) (3.65 m) / (1.01*10^-3 m) = 2.316e-3

    For destructive interference (dark fringes), equation becomes:

    x = (n - 0.5) λ L / d

    Second dark fringe, n = 1.5

    x = 1.5 (641*10^-9 m) (3.65 m) / (1.01*10^-3 m) = 3.47e-3
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