Chapter 19.2, Problem 28SSC

To determine

The grating that has more lines per millimeter.

Explanation of Solution

Introduction:

The bending of light waves around the boundaries of an obstacle and illumines the area where the geometrical shadow of the obstacle is expected is known as diffraction. As the light wave encounters the grating, the wave bends and there will be a diffraction of light waves from the grooves in the grating and interference takes place among the light waves that are diffracted from the grooves. This interference may be constructive or destructive depending on the phase difference between the waves. For constructive interference, the band produced in the pattern is bright and for the destructive interference, the region is dark in the pattern.

The equation which relates the dot spacing in the pattern $\left(x\right)$ and the slit width $\left(d\right)$ of the diffraction grating is given by,

  $\lambda \approx \frac{xd}{L}$

Where, $\lambda$ is the wavelength of light used and $L$ is the separation between the grating and the screen.

This expression says that larger the gaps between the dots in the diffraction pattern, thinner the slit width and hence there will be more number of lines per millimeter in the grating. Here, the dots in the diffraction pattern produced by the first grating are spread out more than that produced by the second. Hence the first grating has more lines per millimeter.