Diffraction and Interference of Light

Shine light through two tiny slits and instead of two bright lines you get a whole row of bright and dark stripes marching across the screen. Light bends as it squeezes through each gap, the two spreading beams overlap, and where they meet they either add up into a bright band or cancel out into a dark one. That simple overlap is the fingerprint of a wave, and it is the strongest everyday clue that light is a wave.

Diffraction: waves spread through gaps

When a wave passes through a narrow gap it does not stay in a tidy beam. It fans out the other side, like ripples spreading after they slip through a gap in a harbour wall. This spreading is called diffraction.

The amount of spreading depends on one thing: how the wavelength compares with the size of the gap.

• When the wavelength is large compared with the gap, the wave spreads out a lot. A big $\lambda / w$ ratio means strong diffraction.
• When the wavelength is small compared with the gap, the wave barely bends at all and carries straight on.

So a wave only really fans out when the gap is roughly its own wavelength or smaller. That is why light, with its tiny wavelength, needs incredibly narrow slits before the spreading becomes obvious.

Interference: two waves overlap

Now send light through two narrow slits side by side. Each slit diffracts the light, so two spreading beams sweep out across the screen and overlap. Where they meet, the waves combine. This is interference, and it is what builds the striped pattern.

There are only two outcomes when the waves meet:

• They arrive in step, peak on peak, and reinforce. The light is bright. This is constructive interference.
• They arrive out of step, peak on trough, and cancel. The screen is dark. This is destructive interference.

Whether a point is bright or dark comes down to the path difference, the extra distance one wave travels compared with the other to reach that point.

The light source on the left sends wavefronts out to both slits at once, so the two slits stay perfectly in step. Each slit then acts as a fresh source, sending its own wavefronts forward (the grey arcs). The two blue lines are the paths from the two slits meeting at one point. Because that point is a whole number of wavelengths from both slits, the waves arrive in step and you get a bright fringe. The red bars show the full pattern of bright bands on the screen.

The bright and dark rule

Everything comes down to the path difference. Count how many wavelengths of extra distance one wave travels compared with the other.

• Bright (constructive) when the path difference is a whole number of wavelengths: $n\lambda$ for $n = 0, 1, 2, \dots$ The centre of the screen ($n = 0$, zero path difference) is the brightest fringe.
• Dark (destructive) when the path difference is a half number of wavelengths: $\left(n + \tfrac{1}{2}\right)\lambda$ for $n = 0, 1, 2, \dots$

A whole number means the peaks line up and reinforce. A half number means a peak meets a trough and they wipe each other out.

How far apart are the fringes?

For Young’s double slit setup there is a neat formula for the gap between one bright fringe and the next:

$\Delta y = \frac{\lambda L}{d}$

Here $\lambda$ is the wavelength, $L$ is the distance from the slits to the screen, and $d$ is the separation between the two slits. The formula works when the screen is much further away than the slits are apart, that is when $L \gg d$, which is almost always the case in the lab.

Read it like a story. A longer wavelength or a further screen spreads the fringes out. Wider slit separation squeezes them back together.

See it for yourself

Drag the sources, change the wavelength and the slit spacing, and watch the bright and dark bands shift. Try widening the slit separation and notice the fringes crowd closer together, then stretch the wavelength and watch them spread back out.

How to actually solve one

The method is a short, repeatable recipe.

1. Convert every length into metres so nothing trips you up later.
2. To decide bright or dark, write the path difference as a multiple of $\lambda$. A whole number is bright, a half number is dark.
3. For fringe spacing, use $\Delta y = \dfrac{\lambda L}{d}$ straight off.
4. Check the answer is sensible. Fringe spacings are usually a few millimetres, not metres.

Keep the wavelength tiny. Visible light sits around $5$ to $7 \times 10^{-7}$ m, so if your $\lambda$ comes out near a metre, something has gone wrong with the unit conversion.

Try one: at a point on the screen, light from the two slits has a path difference of $2.5\lambda$. Is the point bright or dark, and why?

Lock it in with active recall

Cover the answer and say each one out loud before you flip. Rate yourself honestly — the cards you find hard come back sooner, the ones you know are spaced further out.

See the recipe in action in the Worked Examples tab, then test yourself in Try It.