Question

If white light illuminates a diffraction grating having 710 lines/mmlines/mm , over what range of angles does the visible mm

Answer 1

Complete Question

The human eye can readily detect wavelengths from about 400 nm to 700 nm. If white light illuminates a diffraction grating having 710 lines/mm, over what range of angles does the visible m = 1 spectrum extend

Answer:

The  value  $\theta = 16.5 ^ o$

Explanation:

From the question we are told that

   The  diffraction grating haves $a = 710 \ lines /mm$

 

Generally the separation of the slit is mathematically represented  as

      $d = \frac{1}{710} \ mm =0.001408 \ mm = 1.408 *10^{-6} \ m$

 Generally the condition for constructive interference is mathematically represented as  

           $dsin(\theta ) = n \lambda$

So

          $\theta = sin ^{-1} [\frac{n * \lambda }{d} ]$

=>       $\theta = sin^{-1}[\frac{1 * 400 *10^{-9}}{ 1.408*10^{-6}} ]$

=>         $\theta = 16.5 ^ o$