Chapter 19, Problem 55A

To determine

To explain:The differences in the characteristics of the diffraction patterns formed by given diffraction gratings.

Explanation of Solution

Introduction:

Diffraction grating is an optical component that comprises of a surface ruled with an equidistant, closely spaced, parallel lines. These lines in the grating are opaque and the spacing between the lines acts as a number of closely placed slits. They can disperse the light beam passing through it and produce a spectrum of light by the principle of diffraction. The diffraction through the grating depends on the wavelength of light and also on the spacing between the lines in the grating.

The expression which relates the spacing between the lines in the diffraction 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 and $L$ is the distance between the grating and the screen.

The larger the number of lines per cm in the grating, thinner the slit width. Above expression indicates that thinner the slit width, larger the spacing between the lines in the pattern and hence thinner the lines in the diffraction pattern. Therefore the lines in the diffraction pattern produced by diffraction grating containing ${\text{10}}^5\text{ lines/cm}$ are narrower as compared to that formed by the grating containing ${\text{10}}^4\text{ lines/cm}$ .