C.3 · IB Physics
Diffraction grating
See how adding slits sharpens the interference maxima: from broad double-slit fringes to thin bright lines. Change the spacing and wavelength, and add the single-slit envelope.
Predict first
Start from the default settings (N = 2, d = 2.5 μm, λ = 550 nm). If you raise the number of slits N from 2 to 12, what happens to the angle of the first-order maximum?
The maxima obey d sinθ = nλ, which does not contain N. More slits make each maximum narrower and brighter but leave its position unchanged.
Check it in the model: Move the Number of slits N slider from 2 to 12 and watch the First-order angle θ₁ readout stay at 12.7°.
I = I₀ [sin(Nβ) ÷ (N sinβ)]²
β = π d sinθ ÷ λ
half-width ≈ λ ÷ (N d cosθ)
orders: n < d ÷ λ
- First-order angle θ₁
- Orders each side
- Principal maxima in total
- Half-width of 1st-order peak
- Faint maxima between peaks
- Angles of orders 1 to 5
Try this
- Set N = 2, d = 2.5 μm, λ = 550 nm and note the angle of the first order. Raise N to 12. Which features of the pattern change, and which stay put?
- With N = 12 and d = 2.5 μm, compare λ = 450 nm and λ = 650 nm. Which colour is deviated more, and what are the two values of θ₁?
- Keep λ = 550 nm and N = 12, and raise d from 1.5 μm to 5.0 μm. How many orders appear on each side at the two ends, and why?
Exam tip: the maxima obey d sinθ = nλ for any N, so use it to find angles and the highest order (n < d ÷ λ, since sinθ cannot exceed 1); extra slits only make each maximum narrower and brighter.