Diffraction and diffraction gratingsEdexcel A-Level Physics: Revision notes

Diffraction is the spreading of waves as they pass through a gap or round an obstacle. It is most pronounced when the width of the gap is about the same size as the wavelength.

• Gap much larger than λ: waves pass through with very little spreading, leaving a clear shadow
• Gap about λ: strong spreading into the geometric shadow, wavefronts become almost circular

For a fixed gap, a longer wavelength diffracts more. In a ripple tank, raising the frequency at constant speed shortens λ and so reduces diffraction.

Huygens' construction explains wave propagation. Every point on a wavefront acts as a source of secondary wavelets, which spread out in all forward directions at the wave speed. The new wavefront is the envelope of the wavelets.

At a gap, only the wavelets from points in the gap contribute. Near the edges nothing is added from outside, so the wavefront curves round into the geometric shadow. This is diffraction.

A diffraction grating is a plate with a very large number of equally spaced parallel slits, typically hundreds of lines per millimetre. The slit spacing is d = 1 ÷ (lines per metre). For 300 lines per mm, d = 1 ÷ 300 000 = 3.33 × 10⁻⁶ m.

Light diffracted by each slit overlaps and interferes. In certain directions the waves from adjacent slits arrive in phase and give sharp, bright maxima. Between them there is destructive interference. Many slits make the maxima narrow and bright.

A maximum is formed at angle θ to the normal where the path difference between adjacent slits is a whole number of wavelengths:

nλ = d sinθ

where n = 0, 1, 2, ... is the order. The n = 0 maximum is straight ahead.

The highest order occurs as sinθ approaches 1, so n is the largest whole number not exceeding d/λ.

Worked example: d = 1.67 × 10⁻⁶ m and λ = 633 nm gives sinθ = 0.380 for n = 1, so θ = 22.3°. Since d/λ = 2.6, the highest order is n = 2.

With white light the n = 0 maximum is white, because the path difference is zero for every wavelength. For n ≥ 1, sinθ = nλ/d depends on λ, so each order is a spectrum with violet nearest the centre and red furthest out.

Higher-order spectra are wider and can overlap: the third-order violet (about 1200 nm path difference) lies beyond the start of the second-order red at about 1400 nm.

If the grating has more lines per mm (smaller d), the maxima are spread further apart.

1. Fix the grating perpendicular to a laser beam, a known distance D from the screen.
2. Measure the distance between maxima of the same order on both sides of the centre, then halve it to get x.
3. Calculate θ = tan⁻¹(x/D).
4. Use λ = d sinθ ÷ n.
5. Repeat for several orders and plot sinθ against n. The gradient is λ/d.

Measuring across both sides avoids having to find the centre exactly and gives a smaller percentage uncertainty.

Safety: never look into a laser beam or its reflections, and keep the beam below head height.