8.4 The diffraction grating

For a grating with slit spacing d, constructive maxima occur when d sinθ=nλ, where n is an integer order.

Use the grating line density to find d, measure θ from the central maximum and check that |sinθ|≤1.

A 600 lines mm⁻¹ grating has d=1.67 μm; first order at θ=22° gives a wavelength near 6.2×10⁻⁷ m.

n labels bright orders, not the number of slits; the central maximum is n=0.

Use a grating of known line spacing, observe a bright maximum of order n, measure θ and calculate λ=d sinθ/n.

Measure symmetric +n and −n angles where possible, average them, and convert line density to metres per line before substituting.

A laser’s first-order angle on a calibrated grating gives its wavelength; repeating for another colour compares wavelengths directly.

Do not use the angle from the grating normal incorrectly, and do not confuse line density with slit spacing.