Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.310 mm

Question

Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.310 mm. Their interference pattern is observed on a screen 4.40 m from the slits. What is the disatnce on the screen between the first order bright fringe for each wavelength?

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Mộc Miên 3 years 2021-08-11T04:49:27+00:00 1 Answers 15 views 0

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  1. King
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    2021-08-11T04:50:27+00:00
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    Answer:

    0.002699 m or 2.699 mm

    Explanation:

    y = Fringe distance

    d= Distance between slits = 0.310mm

    L = Screen distance = 4.40m

    λ= Wavelength

    Given from question

    λ₁= 660 nm = 6.6 x 10^-9 m

    λ₂= 470 nm = 4.7 x 10^-9 m

    d = 0.340 mm = 3.4 x 10^-3 m

    L = 4.40 m

    In the case of constructive interference, we use below formula

    y/L = mλ/d

    For first order wavelength

    (y₁/4.40) =(1×660×10⁻⁹)/(0.310*10⁻³)

    y₁= (0.310*10⁻³)×(4.40)/(0.310*10⁻³)

    y₁=0.00937m

    (y2/4.40) =(1×470×10⁻⁹)/(0.310*10⁻³)

    y2= =(1×470×10⁻⁹)×(4.40)/(0.310*10⁻³)

    y2=0.00667m

    distance between the fringes is given by (y₁ -y2)

    =0.00937-0.00667=0.002699m

    Therefore, distance on the screen between the first-order bright fringes for the two wavelengths is 0.002699 m or 2.699 mm

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