Question

A diffraction grating is a square 1.0 cm on a side and contains 3500 slits. What is the angle of the first intensity maximum in the diffraction pattern with red light( 660 nm)?

Answer 1

Ans.

The position of the first maximum in the diffraction pattern is given by

$d*sin(\theta) = (1)\lambda \\ \text{d is the slit spacing and }\lambda \text{ is the wavelength of the light} \\ \text{So, the angular position of the first maximum is } sin(\theta) = \frac{\lambda}{d} \\ \text {or }\theta = arcsin\left(\frac{\lambda}{d}\right) \\ \lambda = 660 nm = 660*10^{-9} m \\ \\ \text{The slit spacing d =} \frac{\text{length of grating}}{\text{no. of slits}} \\ \\ \text{The length of the grating= 1.0 cm} \\ \text{No. of slits = 3500} \\ \\ d = \frac{1.0 \ cm}{3500} = 2.86*10^{-4} \ cm = 2.86*10^{-6} \ m \\ \\ \theta = arcsin\left(\frac{660*10^{-9}}{2.86*10^{-6}}\right) = 13.3^{\circ}$

The angle of the first maximum intensity = 13.3 degrees