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14 September, 14:47

In a four-slit experiment the distance between the central bright fringe and the second off-center bright fringe is 8 cm. What is the distance between adjacent dark fringes?

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  1. 14 September, 15:01
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    y' = 2 cm

    Explanation:

    In the system with more than two slits we can consider them a network and diffraction, which is described by the expression

    d sin θ = m λ

    Where d is the separation between the slits, λ the wavelength and m an integer that is the order of diffraction.

    Let's use trigonometry for line separation

    tan θ = y / L

    Where L is the distance to the observation screen, in diffraction and measured angle experiments it is small

    tan θ = sin θ / cos θ = sin θ

    We replace

    d y / L = m λ

    This is the equation for constructive interference, it indicates that y = 8 cm for m = 2

    d 8 / L = 2 λ

    d / Lλ = 2/8

    For the case destructive interference we must increase the length is wave is λ/2, the equation remains

    d y' / L = (m + ½) λ

    In the case of adjacent strips m = 0

    d y' / L = (0 + 1/2) λ

    d / Lλ = 1 / 2y'

    Let's match the two diffraction equations

    ¼ = 1 / 2y'

    2y' = 4

    y' = 2 cm
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