The diffraction grating

A diffraction grating is an optical device made up of a large number of equally spaced parallel slits. When monochromatic light (light of a single wavelength) passes through the grating, it is diffracted by each slit, and the diffracted waves interfere to produce a pattern of bright and dark fringes on a screen.

The bright fringes, called maxima, occur at specific angles where the path difference between light from adjacent slits is an integer multiple of the wavelength. This constructive interference produces sharp, bright lines at certain angles.

Grating Equation

The condition for constructive interference (maxima) is given by the grating equation:

The grating spacing $d$ is usually given by $d = \frac{1}{N}$, where $N$ is the number of lines per metre on the grating.

Using a Diffraction Grating to Measure Wavelength

1. Shine monochromatic light perpendicularly onto the grating.
2. Observe the diffraction pattern on a screen or detector.
3. Measure the angle $\theta$ at which each bright fringe (maximum) appears.
4. Use the known value of $d$ (from the grating's specification) and the measured $\theta$ in the grating equation to calculate the wavelength $\lambda$.

Key Points

• The central maximum ($n=0$) is always at $\theta = 0^\circ$.
• Higher order maxima ($n=1,2,...$) occur at larger angles.
• The maximum possible value of $n$ is limited by $\sin \theta \leq 1$.

Summary

• A diffraction grating produces sharp maxima at angles given by $d \sin \theta = n\lambda$.
• Measuring the angle of these maxima allows the wavelength of light to be determined accurately.