The diffraction grating Cambridge International AS & A Level Physics revision
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In plain words
A diffraction grating is a slide with thousands of slits ruled side by side. Instead of blurry stripes it sends each colour off in a few sharp, bright beams at exact angles. Measure an angle and you get the wavelength very precisely. It is how we know what the stars are made of.
4 things to know
- d sin θ = nλ, where d is the spacing between neighbouring slits, θ is the angle of a beam from straight ahead, and n is the order of that beam (0, 1, 2 ...).
- d = 1 ÷ (number of lines per metre).
- The highest order that exists is the largest whole number n for which nλ ÷ d is not more than 1, because sin θ can't be bigger than 1.
- Longer wavelengths are sent off at bigger angles, so a grating spreads white light into a spectrum in every order except n = 0.
Worked example
Light passes through a diffraction grating with 300 lines per mm, and the first-order beam is at 10.4° to straight ahead. Find the wavelength.
- d = 1 ÷ 300 mm = 3.33 × 10⁻⁶ m.
- d sin θ = nλ with n = 1: λ = 3.33 × 10⁻⁶ × sin 10.4°.
- = 6.0 × 10⁻⁷ m (600 nm).
Tips and tricks
- Turn lines per millimetre into lines per metre before you find d: 300 per mm is 3.00 × 10⁵ per m.
- For a better angle, measure the angle between the two first-order beams, one on each side, and halve it.
It lands in your notebook with its questions as flashcards.
The diffraction grating: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
A grating has 500 lines per mm. What is the slit spacing d?
1 ÷ (5.0 × 10⁵ lines per metre).
In d sin θ = nλ, what is n?
n = 0 is straight ahead, n = 1 is the first beam on either side.
White light passes through a grating. Which colour is sent off at the largest angle in the first order?
Red has the longest wavelength.
White light passes through a grating. What is seen straight ahead, at n = 0?
Every wavelength has θ = 0 there, so the colours are not separated.
A grating is swapped for one with more lines per millimetre. What happens to the angle of the first-order beam?
A smaller d means a larger sin θ.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 9 marks. Write your answers on paper, then check them.
The diffraction grating
Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org
Name ______________________________ Date ______________
Light of wavelength 600 nm falls on a grating with a slit spacing of 3.33 × 10⁻⁶ m. Find the highest order that can be seen.[3]
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5. d ÷ λ = 5.55, and n must be a whole number.
Light of wavelength 500 nm falls on a grating with 400 lines per mm. Find the angle of the second-order beam.[3]
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23.6°. d = 2.5 × 10⁻⁶ m, so sin θ = 2 × 5.0 × 10⁻⁷ ÷ 2.5 × 10⁻⁶ = 0.40.
Describe how to find the wavelength of laser light with a diffraction grating.[3]
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Shine the laser at right angles through the grating on to a screen a measured distance D away. Measure the distance between the two first-order spots and halve it to get y. Then tan θ = y ÷ D gives θ, and λ = d sin θ, with d found from the number of lines per metre.
Answers: The diffraction grating
- 1. 5. d ÷ λ = 5.55, and n must be a whole number.
- 2. 23.6°. d = 2.5 × 10⁻⁶ m, so sin θ = 2 × 5.0 × 10⁻⁷ ÷ 2.5 × 10⁻⁶ = 0.40.
- 3. Shine the laser at right angles through the grating on to a screen a measured distance D away. Measure the distance between the two first-order spots and halve it to get y. Then tan θ = y ÷ D gives θ, and λ = d sin θ, with d found from the number of lines per metre.