Diffraction gratingsEdexcel International A Level Physics: Revision notes
Section 1
The diffraction grating
A diffraction grating is a plate with a very large number of equally spaced parallel slits. The slit spacing d is the distance between the centres of adjacent slits, found from the number of lines per unit length: d = 1/N. For 300 lines per mm, d = 1/300 000 m = 3.33 × 10⁻⁶ m.
When monochromatic light of wavelength λ passes through at normal incidence, each slit diffracts the light and the waves from all the slits superpose. Sharp, bright maxima are seen in certain directions, with darkness between them.
Convert lines per millimetre correctly: 600 lines per mm means d = 1/600 000 m, not 1/600 m.
Section 2
The grating equation
Waves from adjacent slits reach a distant screen with a path difference of d sin θ. They reinforce, giving a maximum, when this equals a whole number of wavelengths:
nλ = d sin θ
Here n = 0, 1, 2, … is the order of the maximum and θ is the angle between the central maximum and that order. The n = 0 maximum is straight ahead and the same for all wavelengths.
Worked example. λ = 633 nm, d = 3.33 × 10⁻⁶ m, n = 1: sin θ = 0.190, so θ = 10.9°. For n = 2, sin θ = 0.380 and θ = 22.3°.
Section 3
Highest order and white light
Since sin θ cannot exceed 1, the largest possible order is the whole number below d/λ. In the example above, d/λ = 5.3, so only orders up to 5 on each side are seen.
For white light, each wavelength has a different angle for the same order, so the maxima of orders above zero are spectra. The central maximum is white, and in each spectrum violet (shortest λ) is nearest the centre and red (longest λ) is furthest. Higher orders are wider and may overlap: for d = 2.0 × 10⁻⁶ m, third-order violet appears at 37° and second-order red at 44°.
A smaller slit spacing d gives larger angles, so the maxima are more widely separated but fewer orders are seen.
Section 4
Core Practical 6: wavelength of laser light
Direct a laser at right angles to a grating, with a screen a long way behind it. Measure the grating-to-screen distance L and the distance x from the central maximum to a chosen order, using the spots on both sides and halving the separation.
Then tan θ = x / L, so λ = d sin θ / n. Repeat for several orders, or plot sin θ against n, which gives a line of gradient λ/d. A larger L makes the measurement of x relatively more precise.
Safety: never look into the beam, and do not allow reflections to reach anyone's eyes.
Use tan θ = x / L to find θ, then sin θ in the grating equation. Do not use x / L as sin θ unless θ is tiny.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Diffraction gratings
- A student shines a red laser beam of wavelength 633 nm at normal incidence on a diffraction grating that has 300 lines per millimetre. A series of bright spots, called maxima, is formed on a distant screen.Calculate the highest order of maximum that can be seen on the screen.2 marks
- White light containing wavelengths from 400 nm (violet) to 700 nm (red) is directed at normal incidence at a diffraction grating with slit spacing 2.00 × 10⁻⁶ m. The light is then observed on a screen a long way from the grating.Calculate the angular separation between the first-order maxima for red light of wavelength 700 nm and violet light of wavelength 400 nm.2 marks
- In Core Practical 6 a student determines the wavelength of light from a laser. She uses a diffraction grating with 600 lines per millimetre at normal incidence, and places a screen 2.50 m from the grating. The first-order maximum is found 1.06 m from the central maximum on the screen.Describe how the student should set up the apparatus and take measurements so that she can calculate the wavelength accurately.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).