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Sunlight is incident on a diffraction grating that has 3,550 lines/cm. The second-order spectrum over the...

Sunlight is incident on a diffraction grating that has 3,550 lines/cm. The second-order spectrum over the visible range (400-700 nm) is to be limited to 2.05 cm along a screen that is a distance L from the grating. What is the required value of L?

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Answer #1

U

The distance between the lines in meteris

      d = 1cm / 3550 =10-2 m / 3550

         =2.8169*10-6 m

using the formula

   d Sin θ = m λ

   θred = Sin-1 ( 2λred / d ) = sin-1[ 2*700nm / d]

           =22.65o

θviolet = 12.71o

The required value of L is

    L = Δ y / [ tanθred -tanθviolet ]

       = 2.05 cm / [ tan22.65 - tan12.71]

        =10.69 cm.

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