Diffraction

Airy disc from a pinhole

A round hole makes a bright central disc ringed by faint circles: the Airy pattern. Every lens and telescope has a round aperture, so this pattern sets the smallest detail they can show.

What you are looking at

The screen shows the disc with its first dark ring at about 3.5 mm radius.

How the bench is set up

HeNe laser with a 1 mm waist, a pinhole of 0.2 mm diameter, a screen 900 mm away.

The theory

A circular aperture of diameter $D$ gives

I(\theta) = I_0\left[\frac{2J_1(x)}{x}\right]^2, \qquad x = \frac{\pi D\sin\theta}{\lambda},

with its first zero at $\sin\theta = 1.22\,\lambda/D$ . Two stars closer than that cannot be told apart: the Rayleigh criterion.

What to measure

First dark ring at 1.22 λL/D

Measure the radius of the first dark ring.
Compare with $1.22\lambda L/D$ = 3.47 mm.

What the model leaves out

The pinhole is lit by a nearly uniform part of the beam.

Things to try

Halve the pinhole and the disc doubles.
Swap the pinhole for a disc (an obstacle) and look for the bright Arago spot at the centre of its shadow.

References

E. Hecht (2017), Optics, 5th edition, Pearson.
G. B. Airy (1835), On the diffraction of an object-glass with circular aperture, Transactions of the Cambridge Philosophical Society 5, 283.

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