Question

Light from a laser strikes a diffraction grating that has 5 308 grooves per centimeter. The central and first-order principal maxima are separated by 0.488 m on a wall 1.88 m from the grating. Determine the wavelength of the laser light. (In this problem, assume that the light is incident normally on the gratings.) nm

Answer 1

Solution :

Given :

The angle of the first maximum with the center is given by :

$a=\tan^{-1}\left(\frac{0.488}{1.88}\right)$

  = 14.5°

The grating distance can be calculated as :

$d=\frac{1 \ cm}{5308 \text{ slits}}$

   = $1.88 \times 10^{-4} \ m$

When the principal maxima yields at y = 0.488 m and the length from the wall 1.88 m. Thus the equation of the wavelength is :

$\lambda = g \times \frac{\sin a}{n}$  ,       where n = 1

  $=1.88 \times 10^{-4} \times \sin (14.5)$

 $=4.70 \times 10^{-5} \ m$