Question

A light with a second-order dark band forms a diffraction angle of 20.0 degrees. The diffraction grating has 200.0 lines per mm. The wavelength of the light, to the nearest whole number, is _____ nm.

Answer 1

Answer:

The value is $\lambda = 684 \ nm$

Explanation:

From the question we are told that

     The order of the dark fringe is  m  =  2

      The diffraction angle is  $\theta = 20^o$

       The diffraction grating is  $l = 200\ lines\ per\ mm \ = \ 200000\ lines\ per\ m$

Generally separation between the slits is mathematically represented as

        $d = \frac{1}{ 200000}$

=>      $d = 5 *10^{ -6} \ m$

Generally the condition for destructive interference is mathematically represented as

            $dsin(\theta ) = (m - \frac{1}{2} ) \lambda$

=>    $5 *10^{-6} sin(20) = [2 + \frac{1}{2}] * \lambda$

=>   $\lambda = 684 *10^{-9} \ m$

=>   $\lambda = 684 \ nm$

Answer 2

Answer:

684

Explanation:

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