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30 January, 05:01

Coherent light of frequency 6.34 x 10^14 Hz passes through two thin slits and falls on a screen 82.0 cm away. You observe that the third bright fringe occurs at ± 3.09 cm on either side of the central bright fringe.

(a) How far apart are the two slits?

(b) At what distance from the central bright fringe will the third dark fringe occur?

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  1. 30 January, 05:25
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    a) d = 3.76 10⁻⁵ m, b) y = 3.61 10⁻² m

    Explanation:

    The interference phenomenon is described by the expression

    d sin θ = m λ

    Where d is the separation of the slits, λ the wavelength and m an integer indicating the interference number

    Let's apply to this case, as we observe the third order m = 3

    a) Let's use trigonometry to find the angles

    tan θ = y / x

    The phenomena of interference and diffraction angles are very small, so

    tan θ = sin θ / cos θ = sin θ

    sin θ = y / x

    We replace

    d y / x = m λ

    d = m λ x / y

    The frequency of the light is

    c = λ f

    λ = c / f

    Let's calculate

    λ = 3 10⁸ / 6.34 10¹⁴

    λ = 4.73 10⁻⁷ m

    d = 3 4.73 10⁻⁷ 0.820 / 0.0309

    d = 376.56 10⁻⁷ m

    d = 3.76 10⁻⁵ m

    b) for destructive interference we must add ½ Lam

    d sin θ = (m + ½) λ

    d y / x = (m + ½) λ

    y = (m + ½) λ x / d

    Let's calculate

    y = (3 + ½) 4.73 10⁻⁷ 0.820 / 3.76 10⁻⁵

    y = 3.61 10⁻² m
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