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Core idea

A diffraction grating has many equally spaced parallel slits. Bright principal maxima occur when the path difference between adjacent slits is an integer number of wavelengths:

$n\lambda=d\sin\theta$

Here, $n$ is the order number $0,1,2,\ldots$ , $\lambda$ is the wavelength, $d$ is the spacing between adjacent slits, and $\theta$ is measured from the central maximum to the chosen maximum.

Build the model

If a grating has $N$ lines per metre, the slit spacing is $d=1/N$ . For a selected maximum, identify its order $n$ , convert $d$ and $\lambda$ to consistent units, and solve for the unknown angle, wavelength or spacing. The central maximum is $n=0$ ; the first maxima on either side are $n=1$ .

Check the allowed orders

Because $\lvert\sin\theta\rvert\le 1$ , a wavelength can only produce orders satisfying $n\lambda\le d$ . The largest possible order is therefore the greatest integer not exceeding $d/\lambda$ . For overlapping wavelengths, equate their path-difference conditions: if the second-order maximum of $\lambda_1$ coincides with the third-order maximum of $\lambda_2$ , then $2\lambda_1=3\lambda_2$ .

Common trap

Do not use the number of lines per metre as $d$ ; invert it first. Do not count the central maximum as first order, and do not replace the grating equation with the small-angle approximation unless the question explicitly permits that approximation.

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Monochromatic light of wavelength $\lambda$ is incident normally on a diffraction grating. The adjacent lines of the diffraction grating are separated by a distance of $2.8 \lambda$ . How many diffraction maxima are present in the transmitted light?

The HL extension is secure when you can model diffraction as interference and read the limits of the pattern.

Single-slit diffraction: b sinθ = nλ for minima
Diffraction envelopes in multiple-slit patterns
Diffraction grating maxima: nλ=d sinθ
Allowed orders satisfy nλ≤d

C.3.14 (HL)—Diffraction gratings

Model Diffraction Gratings

Retrieve the HL C.3 Wave Phenomena Model

C.3.14 (HL) Exam Analysis