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# Young's double slit experiment

## Young's double-slit experiment

Young's double-slit experiment, first performed by the scientist Thomas Young in the early 19th century, was one of the first demonstrations of the wave nature of light.

In the experiment, a beam of monochromatic, coherent light is passed through a double-slit. This produces alternating bright and dark bands (or fringes) on a screen corresponding to the interference pattern of the light waves.

This meant that light had diffracted through each slit and had undergone interference, showing that light was indeed a wave.

Comparison of the diffraction patterns produced by a laser beam diffracting through a single slit (left) and a double-slit (right).

## Central maximum

The area around the midpoint of the two slits in Young's double-slit experiment is a region of constructive interference (called the central maximum.

At the midpoint, there is no difference in the path of the wave trains which travel from each slit (i.e. they arrive in phase). This corresponds to a point of perfect constructive interference.

The wave trains that arrive at the points slightly to the left and right of the central maximum are slightly out of phase. The intensity of the light within the central maximum therefore decreases with distance from the midpoint.

## Maxima

Bright fringes (or maxima) occur around the points where the path difference is an integer multiple of the wavelength (i.e. $\Delta x=\lambda$, $2\lambda$, $3\lambda$, ... , $n\lambda$).

The waves that arrive at these points are in phase and undergo perfect constructive interference.

Similar to the central maximum, the wave trains arriving at points within the fringes that are slightly to the left and right of the point of perfect constructive interference are slightly out of phase.

The intensity of the light within the maxima therefore decreases with distance from the points of perfect constructive interference.

These maxima are found symmetrically on both sides of the central maximum, are equally spaced and follow a decreasing pattern of brightness with distance from the central maximum.

The fringes decrease in overall brightness with distance from the central maximum as the distance that the wave trains have to travel to reach the screen is greater. This means that the wave becomes more diffuse (lower intensity) as the distance increases.

## Minima

Dark fringes (or minima) occur around the points where the path difference is an odd integer multiple of a half-wavelength (i.e. $\Delta x=\lambda/2$, $3\lambda/2$, $5\lambda/2$, ... , $n\lambda/2$).

This is because the waves would arrive at these points $\pi$ radians out of phase (corresponding to odd integer multiples of a half-wavelength). This means that the wave trains undergo perfect destructive interference at these points.

The wave trains arriving at points within the fringes that are slightly to the left and right of the point of perfect destructive interference are slightly more in phase.

The intensity of the light within the minima therefore increases with distance from the points of perfect destructive interference.

The minima are found between any two adjacent maxima and symmetrically on both sides of the central maximum.

## Double-slit equation

The wavelength $\lambda$ of the monochromatic light coming from the source is given by: $$\lambda=\frac{ax}{D}$$ $a$ is the slit separation, $x$ is the distance between fringes and $D$ is the distance between the double-slit and the screen.

This formula is derived by considering the phase difference between the wave trains coming from each slit and determining the spacing of fringes on a screen.