Question

The human eye can readily detect wavelengths from about 400 nm to 700 nm. Part A If white light illuminates a diffraction grating having 910 lines/mm , over what range of angles does the visible m

Answer 1

Answer:

The correct answer is "$21.344^{\circ}$" and "$39.56^{\circ}$".

Explanation:

According to the question,

Slit width,

$d=\frac{1}{910 \ lines/mm}$

  $=\frac{1}{910\times 10^3}$

  $=1.099\times 10^{-6} \ m$

The condition far first order maxima will be:

⇒ $d Sin \theta = 1 \lambda$

Now,

⇒ $\Theta_{min} = Sin^{-1} (\frac{\lambda}{d} )$

             $=Sin^{-1} (\frac{400\times 10^{-9}}{1.099\times 10^{-6}} )$

             $=21.344^{\circ}$

⇒ $\Theta_{max} = Sin^{-1} (\frac{\lambda}{d} )$

             $=Sin^{-1} (\frac{700\times 10^{-9}}{1.099\times 10^{-6}} )$

             $=39.56^{\circ}$