Single slit diffraction

Diffraction is the spreading out of a wave when passing through a gap in a boundary. It is optimised when the width of the gap is similar in magnitude to the wavelength of the wave. With a small enough gap we can diffract visible light.

X-rays have an even smaller wavelength than visible light. These diffract on an atomic scale, enabling materials scientists to determine the structure of crystals. 


Key Concepts

A laser is shone through a rectangular slit onto a screen.

We might expect the screen to be brightest in the centre and for the laser light to reduce in intensity outwards. In fact, the pattern is not so simple: the brightness minimises before increasing again. We can plot a graph of intensity against distance from the centre.

The diffraction pattern is formed by summing together to vector components of all parts of the wave, which have travelled different distances to each point on the screen.

Equation

We can determine the position of the first minimum using the approximation equation:

\(\theta = {\lambda \over a}\)

  • \(\theta\) is the angle subtended at the slit by the first minimum and the centre (rad)
  • \(\lambda\) is the wavelength of the light (m)
  • \(a\) is the width of the slit (m)

Since the angle is small, we can also state that it is approximately equal to the ratio of the distance to the minimum and the distance from the slit to the screen:

\(\theta = {y\over D}\)

  • \(y\) is the distance between the centre and the first minimum (on either side since symmetrical) (m)
  • \(D\) is the distance from the slit to the screen (m)

Maxima intensity ratios

The central maximum has the highest intensity, \(I_0\). The next maximum has intensity \(\approx {I_0\over22} \) with the following \(\approx {I_0\over63} \). The Subject Guide is unclear here, stating that students should know approximate ratios of successive maxima intensities.

Wondering where these come from? Check out the section Single Slit Peak Intensities here.

Essentials

Monochromatic light

The equation for the first minimum indicates that the angle is increased by increasing the wavelength of light. Red light produces a broader pattern than green and blue light when passing through the same slit.

White light

White light contains all the wavelengths of visible light. Because the angle to the first minimum is affected by wavelength, the colours of light separate.

This is not evident in the central maxium as all wavelengths have travelled the same distance and so the vector components add to give the original combination. However, outward from the centre, the colours of light separate continuously as their wavelengths form maxima at slightly different angles. Blue light is nearest the centre and red outermost.

Test Yourself

Use quizzes to practise application of theory.


START QUIZ!
MY PROGRESS

How much of Single slit diffraction have you understood?