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30 March, 18:30

A two-slit pattern is viewed on a screen 1.26 m from the slits. If the two fourth-order maxima are 53.6 cm apart, what is the total width of the central bright fringe?

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  1. 30 March, 18:47
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    = 6.55cm

    Explanation:

    Given that,

    distance = 1.26 m

    distance between two fourth-order maxima = 53.6 cm

    distance between central bright fringe and fourth order maxima

    y = Y / 2

    = 53.6cm / 2

    = 26.8 cm

    =0.268 m

    tan θ = y / d

    = 0.268 m / 1.26 m

    = 0.2127

    θ = 12°

    4th maxima

    d sinθ = 4λ

    d / λ = 4 / sinθ

    d / λ = 4 / sin 12°

    d / λ = 19.239

    for first (minimum)

    d sinθ = λ / 2

    sinθ = λ / 2d

    = 1 / 2 (19.239)

    = 1 / 38.478

    = 0.02599

    θ = 1.489°

    tan θ = y / d

    y = d tan θ

    = 1.26 tan 1.489°

    = 0.03275

    the total width of the central bright fringe

    Y = 2y

    = 2 (0.03275)

    = 0.0655m

    = 6.55cm
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