Diffraction

Young’s double slit

Two slits, 40 micrometres wide and a quarter of a millimetre apart, and a screen 900 mm away. Light from the two slits overlaps and makes evenly spaced fringes, inside the wider pattern that each slit makes on its own.

What you are looking at

The screen’s card shows the pattern with real distances. The fringes are about 2.3 mm apart; the envelope’s first zeros are about 14 mm either side of the centre.

How the bench is set up

HeNe laser with a 0.6 mm waist, a double slit (width a = 0.04 mm, separation d = 0.25 mm) and a screen 900 mm behind it.

The theory

In the far field the intensity at angle $\theta$ is

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

so bright fringes come every $\lambda L/d$ on a screen at distance $L$ , and the envelope has zeros at $a\sin\theta = m\lambda$ . The lab computes the pattern by Fresnel propagation, not from this formula, and the two agree.

What to measure

Fringe spacing λL/d inside an envelope with zeros at λL/a

Open the screen card and measure the fringe spacing.
Compare it with $\lambda L/d$ = 2.28 mm.
Count the fringes inside the central envelope: about $2d/a$ .

What the model leaves out

The slits are perfect openings in an infinitely thin screen.

Things to try

Halve the separation: the fringes double in spacing.
Narrow the slits: the envelope widens.
Move the screen to 100 mm and see the near-field pattern.

References

E. Hecht (2017), Optics, 5th edition, Pearson.
T. Young (1804), The Bakerian Lecture: experiments and calculations relative to physical optics, Philosophical Transactions 94, 1.

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