Double slit and the diffraction grating

Last time

Before we start: last time, in Progressive waves and the wave equation, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Light that makes stripes

In 1801 Thomas Young shone light through two narrow slits and saw stripes on a screen. Bright bands and dark bands, evenly spaced. A stream of particles would give two bright lines. Stripes are the signature of waves, and we can use them to measure the wavelength of light.

Double-slit experiment

Light from a single source falls on two narrow slits. Each slit diffracts the light, and the two waves overlap on a screen. The slits act as two coherent sources, because they come from the same wavefront. A bright fringe forms where the path difference is a whole number of wavelengths. A dark fringe forms at an odd number of half wavelengths. The fringes are equally spaced, with separation x.

The equation

The wavelength lambda, the slit separation a, the screen distance D and the fringe separation x are linked. The equation is lambda equals a x over D, or equivalently x equals lambda D over a. Valid when a is much smaller than D. Fringe separation grows with wavelength and with D, and shrinks with larger a. Red light has a longer wavelength than blue, so its fringes are further apart.