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 [tex]\theta = 16.5 ^ o[/tex]
Explanation:
From the question we are told that
The diffraction grating haves [tex]a = 710 \ lines /mm[/tex]
Generally the separation of the slit is mathematically represented as
[tex]d = \frac{1}{710} \ mm =0.001408 \ mm = 1.408 *10^{-6} \ m[/tex]
Generally the condition for constructive interference is mathematically represented as
[tex]dsin(\theta ) = n \lambda[/tex]
So
[tex]\theta = sin ^{-1} [\frac{n * \lambda }{d} ][/tex]
=> [tex]\theta = sin^{-1}[\frac{1 * 400 *10^{-9}}{ 1.408*10^{-6}} ][/tex]
=> [tex]\theta = 16.5 ^ o[/tex]
