What is a diffraction grating?

A diffraction grating is a plate ruled with a very large number of equally spaced parallel lines, so that light passing through the clear spaces between them is diffracted and interferes to give sharp beams in particular directions.

A grating has 300 lines per millimetre. Calculate the grating spacing d.

d = 1/(3.00 × 10⁵ lines per metre) = 3.33 × 10⁻⁶ m, and 3.00 × 10⁵ × 3.33 × 10⁻⁶ returns 1 metre of grating as required.

What does the number n represent in the diffraction grating equation?

It is the order of the diffracted beam, the whole number of wavelengths of path difference between light from adjacent slits, with n = 0 for the straight-through beam.

CCEA A-Level Physics 1210

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Superposition, Interference and Diffraction

The diffraction grating

3 things to know
Unit AS 2

Overview

Recall questions on what a grating is and the equation d sin θ = nλ, calculating the grating spacing from lines per millimetre, what the order number means, worked angle and wavelength calculations, why grating beams are sharper than double-slit fringes, measuring the angle on both sides, and the white-light spectra a grating produces.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the diffraction grating equation, defining every symbol with its unit.

Numbers

Light of wavelength 600 nm passes through a grating with 300 lines per millimetre. Calculate the angle of the first order beam.

Numbers

Light of wavelength 500 nm passes through a grating with 600 lines per millimetre. Calculate the angle of the second order beam.

Questions from this subtopic

Each one with the model answer underneath.

1
What is a diffraction grating?
Model answer
A diffraction grating is a plate ruled with a very large number of equally spaced parallel lines, so that light passing through the clear spaces between them is diffracted and interferes to give sharp beams in particular directions.
2
State the diffraction grating equation, defining every symbol with its unit.
Model answer
d sin θ = nλ, where d is the distance between the centres of adjacent slits in metres, θ is the angle of the diffracted beam from the straight-through direction, n is the whole-number order of the beam and λ is the wavelength in metres.
3
A grating has 300 lines per millimetre. Calculate the grating spacing d.
Model answer
d = 1/(3.00 × 10⁵ lines per metre) = 3.33 × 10⁻⁶ m, and 3.00 × 10⁵ × 3.33 × 10⁻⁶ returns 1 metre of grating as required.
4
What does the number n represent in the diffraction grating equation?
Model answer
It is the order of the diffracted beam, the whole number of wavelengths of path difference between light from adjacent slits, with n = 0 for the straight-through beam.
5
Light of wavelength 600 nm passes through a grating with 300 lines per millimetre. Calculate the angle of the first order beam.
Model answer
sin θ = nλ/d = (1 × 6.00 × 10⁻⁷)/3.33 × 10⁻⁶ = 0.180, so θ = 10.4°, and 3.33 × 10⁻⁶ × sin 10.4° returns 6.0 × 10⁻⁷ m as given.
6
Light of wavelength 500 nm passes through a grating with 600 lines per millimetre. Calculate the angle of the second order beam.
Model answer
d = 1.67 × 10⁻⁶ m and sin θ = (2 × 5.00 × 10⁻⁷)/1.67 × 10⁻⁶ = 0.600, so θ = 36.9°, and 1.67 × 10⁻⁶ × sin 36.9° ÷ 2 returns 5.0 × 10⁻⁷ m.

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