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

Given :

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

`$a=\tan^(-1)\left((0.488)/(1.88)\right)$`

= 14.5°

The grating distance can be calculated as :

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

=
`$1.88 * 10^(-4) \ m$`

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 :

`$\lambda = g * (\sin a)/(n)$` , where n = 1

`$=1.88 * 10^(-4) * \sin (14.5)$`

`$=4.70 * 10^(-5) \ m$`