If the first-order maximum for monochromatic light falling on a double slit is at an angle of 10.0∘, at what angle is the second-order maxim

Question

If the first-order maximum for monochromatic light falling on a double slit is at an angle of 10.0∘, at what angle is the second-order maximum?

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Khang Minh 2 months 2021-08-01T01:05:19+00:00 1 Answers 6 views 0

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    2021-08-01T01:07:12+00:00

    Answer:

    The  value is  \theta_2  = 20.322^o

    Explanation:

    From the question we are told that

      The angle of the first order maximum is  \theta _1  =  10.0^o

    Generally the condition for constructive interference is  

         dsin\theta =  n \lambda

    Here  d is the separation between the slit ,

    n  is the order of maxima  with values n  =  1, 2 , 3 … for first , second , third … order of maxima

        Now for first order of maximum

            dsin\theta_1 =  \lambda \  \   ... \   \ ( 1)

    =>      dsin(10) =  \lambda \  \   ... \   \ ( 1)

        Now for second order of maximum

           dsin\theta =  2\lambda \  \   ... \   \ ( 2)

    dividing equation 1  by 2

          \frac{d sin (10)}{d sin (\theta_2 )} =    \frac{\lambda}{2\lambda}

         \frac{ sin (10)}{ sin (\theta_2 )} =    \frac{1}{2}

    =>   2sin(10) =  sin (\theta_2 )

    =>    0.3473 =  sin(\theta_2)

    =>   \theta_2  =  sin^{-1} [0.3473]

    =>   \theta_2  = 20.322^o

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