A light source shines light consisting of two wavelengths, λ1 = 540 nm (green) and λ2 = 450 nm (blue), on two slits separated by 0.180 mm. T

Question

A light source shines light consisting of two wavelengths, λ1 = 540 nm (green) and λ2 = 450 nm (blue), on two slits separated by 0.180 mm. The two overlapping interference patterns, one from each wavelength, are observed on a screen 1.53 m from the slits. What is the minimum distance (in cm) from the center of the screen to a point where a bright fringe of the green light coincides with a bright fringe of the blue light?

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RobertKer 4 years 2021-08-02T23:20:24+00:00 1 Answers 49 views 0

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  1. Doris
    0
    2021-08-02T23:22:16+00:00
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    Answer:

    The maximun distance is  z_1 = z_2 = 0.0138m

    Explanation:

        From the question we are told that

           The wavelength are  \lambda _ 1 = 540nm (green) = 540 *10^{-9}m

                                               \lambda_2 = 450nm(blue) = 450 *10^{-9}m

            The distance of seperation of the two slit is d = 0.180mm = 0.180 *10^{-3}m

            The distance from the screen is D = 1.53m

    Generally the distance of the bright fringe to the center of the screen is mathematically represented as

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

       Where m is  the order of the fringe

    For the first wavelength  we have

            z_1 = \frac{m_1 (549 *10^{-9} * (1.53))}{0.180*10^{-3}}

                 z_1=0.00459m_1 m

                     z_1= 4.6*10^{-3}m_1 m ----(1)

    For the second  wavelength  we have              

            z_2 = m_2 \frac{450*10^{-9} * 1.53 }{0.180*10^{-3}}

            z_2 = 0.003825m_2

            z_2 = 3.825 *10^{-3} m_2 m  —-(2)

    From the question we are told that the two sides coincides with one another so

                zy_1 =z_2

             4.6*10^{-3}m_1 m = 3.825 *10^{-3} m_2 m

              \frac{m_1}{m_2} = \frac{3.825 *10^{-3}}{4.6*10^{-3}}

    Hence for this equation to be solved

           m_1 = 3

    and  m_2 = 4

    Substituting this into the  equation

                          z_1 = z_2 = 3 * 4.6*10^{-3} = 4* 3.825*10^{-3}

          Hence z_1 = z_2 = 0.0138m

                           

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