A beam of yellow light is made to pass through two slits that are 3.0 x 10−3 meters apart. On a screen 2.0 meters away from the slits, an in

Question

A beam of yellow light is made to pass through two slits that are 3.0 x 10−3 meters apart. On a screen 2.0 meters away from the slits, an interference pattern appears with bands of light separated by 3.9 x 10−4 meters. What is the wavelength of the light?

3.6 x 10−8 m
5.9 x 10−7 m
6.5 x 10−7 m
3.9 x 10−6 m

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Thiên Hương 3 years 2021-07-30T16:46:14+00:00 1 Answers 44 views 0

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  1. Edana
    0
    2021-07-30T16:47:39+00:00
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    Answer:

    5.9\cdot 10^{-7}m

    Explanation:

    The formula to calculate the position of the m-th maximum in the interference pattern produced by the diffraction of light from a double slit is

    y_m=\frac{m \lambda D}{d}

    where

    y is the distance of the maximum from the central bright fringe

    m is the order of the maximum

    \lambda is the wavelength of the light

    D is the distance of the screen from the slits

    d is the distance between the slits

    Here we have:

    d=3.0\cdot 10^{-3} m (distance between slits)

    D = 2.0 m (distance of the screen)

    y=3.9\cdot 10^{-4} m is the distance of the 1st maximum after the central maximum from the central fringe (therefore, taking m = 1)

    Solving for \lambda, we find the wavelength:

    \lambda=\frac{yd}{mD}=\frac{(3.9\cdot 10^{-4})(3.0\cdot 10^{-3})}{(1)(2.0)}=5.9\cdot 10^{-7}m

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