3.3.2.2WavesCore

Diffraction

When a wave passes through a gap or around an edge it $spreads out$ — this is $diffraction$ . A single slit produces a characteristic bright-centre pattern, while a $diffraction grating$ — thousands of slits — sharpens that into precise, well-separated maxima that let us measure wavelengths and split light into spectra.

40 min Video by Science Shorts 3.3.2 Refraction, diffraction and interference

Diffraction (Young’s Double Slit & Grating) — A-Level & GCSE PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Describe the diffraction of waves through a single slit
Describe the single-slit intensity pattern (central maximum and subsidiary maxima)
Explain how slit width and wavelength affect the amount of diffraction
Use the diffraction-grating equation $d sin θ = nλ$
State applications of diffraction gratings, such as spectral analysis

Diffraction through a single slit

$Diffraction$ is the spreading of a wave as it passes through a gap or around an obstacle. The effect is greatest when the gap is about the same size as the wavelength: a gap much wider than $λ$ barely diffracts, while a gap comparable to $λ$ spreads the wave through a wide angle.

Using monochromatic light on a single narrow slit gives a screen pattern of a very bright, wide $central maximum$ with much dimmer $subsidiary maxima$ either side, separated by dark fringes.

Tip — Maximum diffraction (widest spreading) happens when the gap width ≈ the wavelength.

The single-slit pattern

The $central maximum$ is twice as wide as the other maxima and by far the brightest — most of the light energy arrives there. The subsidiary maxima on each side are much fainter and get fainter still further out.

Making the slit $narrower$ spreads the pattern out — the central maximum becomes wider. Using a $longer wavelength$ (e.g. red rather than blue light) also widens it. So the width of the central maximum increases with $λ$ and decreases with slit width.

1The amount of diffraction increases with wavelength.

2Blue light has a shorter wavelength than red, so it diffracts less.

3The central maximum becomes narrower when switching from red to blue.

AnswerNarrower central maximum with blue light

Tip — Two facts examiners want about the central maximum: it is the brightest, and it is twice the width of the other fringes.

The diffraction grating

A $diffraction grating$ has many thousands of equally spaced slits per metre. Light passing through interferes, and instead of broad fringes you get a few very $sharp, bright maxima$ at angles set by the grating equation. The sharpness and separation make gratings far better than a double slit for accurate measurements.

The slit spacing $d$ is found from the number of lines per metre $N$ : $d = 1/ N$ . The integer $n$ is the $order$ of the maximum ( $n = 0$ is the straight-through central maximum).

d sin θ = nλ

Grating equation (d = slit spacing, θ = angle, n = order).

1Slit spacing

d = \frac{1}{300 per mm} = \frac{1 \times 1 0 ^{- 3}}{300} = 3.33 \times 1 0^{- 6}

2For

n = 1

sin θ = \frac{nλ}{d} = \frac{1 \times 600 \times 1 0 ^{- 9}}{3.33 \times 1 0 ^{- 6}} = 0.180

θ = sin^{- 1} (0.180) = 10.4°

Answer

θ \approx 10.4°

Uses of diffraction gratings

Because the diffraction angle depends on wavelength, a grating $splits light into a spectrum$ — each wavelength emerges at its own angle. This is the basis of $spectrometers$ used to analyse the light from stars and to identify elements from their line spectra.

White light through a grating gives a central white maximum with a full spectrum in each higher order (violet diffracted least, red most). Gratings are also used to check the purity of laser light and in the read-out of CDs and DVDs.

Tip — In a grating spectrum the longer wavelength (red) is diffracted through the larger angle — the opposite ordering to a glass prism.

Equation recap

d sin θ = nλ

Diffraction-grating equation.

d = \frac{1}{N}

Slit spacing from N lines per metre.

n_{m a x} < \frac{d}{λ}

Highest observable order (θ ≤ 90°).

Common mistakes to avoid

Using the number of lines per mm directly as d.

d is the spacing between slits: d = 1/N. Convert lines per mm to lines per metre first, then take the reciprocal.

Thinking the central maximum is the same width as the others.

In single-slit diffraction the central maximum is twice as wide as the subsidiary maxima and much brighter.

Believing more orders are always visible.

Only orders with sin θ ≤ 1 exist. The highest order is the largest integer n with n < d/λ.

Key takeaways

Diffraction is the spreading of a wave through a gap or around an obstacle; greatest when gap ≈ λ.
Single slit: a bright central maximum (twice the width, brightest) with dimmer subsidiary maxima.
A grating gives sharp maxima at d sin θ = nλ, with d = 1/N.
Gratings split light into spectra and are used to identify wavelengths and elements.

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Diffraction

When a wave passes through a gap or around an edge it

spreads out

— this is

diffraction

. A single slit produces a characteristic bright-centre pattern, while a

diffraction grating

— thousands of slits — sharpens that into precise, well-separated maxima that let us measure wavelengths and split light into spectra.

40 min Video by Science Shorts 3.3.2 Refraction, diffraction and interference