Diffraction

Single-slit diffraction

A slit a tenth of a millimetre wide spreads a laser beam into a line of spots. The middle one is twice as wide as the others, and the dark gaps between them fall where light from one half of the slit cancels light from the other.

What you are looking at

The screen shows the central maximum and the weaker side lobes, about 5.7 mm apart at 900 mm.

How the bench is set up

HeNe laser, a 0.1 mm slit and a screen 900 mm away.

The theory

The Fraunhofer pattern of a slit of width $a$ is

I(\theta) = I_0\,\mathrm{sinc}^2\!\left(\frac{\pi a \sin\theta}{\lambda}\right),

with zeros at $a\sin\theta = m\lambda$ for every non-zero integer $m$ .

What to measure

Zeros at a sin θ = mλ

Measure the distance between the first zeros either side of the centre.
Compare with $2\lambda L/a$ = 11.4 mm.

What the model leaves out

The slit edges are ideal and the slit is uniformly lit, which is close because the beam is six times wider.

Things to try

Change the laser to 532 nm and watch the pattern shrink.
Use log brightness on the card to see the faint outer lobes.

References

E. Hecht (2017), Optics, 5th edition, Pearson.

More experiments, and how the lab works, are in the laser lab’s overview.