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30 June, 05:50

In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?

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  1. 30 June, 06:03
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    4.5 x 10⁻6m

    Explanation:

    From the formula given,

    ʎ/d = x/L

    The wavelength of 750 nm will be: 750 x 10⁻⁹ / 2.0 x 10⁻³ 3 = x / 2.0

    Now

    50 x 10⁻⁹ / 2.0 x 10⁻³ 3 = x 2.0 = x = 7.5 x 10⁻⁴m

    The wavelength of 900 nm will be: 900 x 10 ⁻⁹ / 2.0 x 10⁻³ = x / 2.0

    00 x 10 ⁻⁹ / 2.0 x 10⁻³ = x / 2.0 = x = 9.0 x 10⁻⁴

    Then

    9.0 x 10⁻⁴ / 7.5 x 10⁻⁴ = 1.2

    to get to the first integer, 1.3 must be 1.2 is the multiplied 5 times t (which will be a fringe (bright)) which is 6.

    Therefore, what this mean is there will be 6 fringes of wavelength 750 nm and 5 fringes of wavelength 900 nm.

    From the central brightest fringe. the mixing fringe will be 4.5 x 10⁻6m or 4500 nm.
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