Diffraction grating practice

Convert line density, calculate wavelength and angles, and check allowed diffraction orders.

Practise

Find diffraction angle

Light of wavelength 500 nm falls on 600 lines/mm. Find the angle of the order 2 maximum. Give your answer to 3 significant figures.

Plane transmission grating, monochromatic light at normal incidence. θ is measured from the straight-through direction. Use degrees for angles.

Normal incidence on a transmission grating. Diffracted order 2 makes the unknown angle θ to the straight-through normal. The drawn ray uses the question geometry; measure no values from the sketch.

Larger diagram

Treat the given values as exact unless an uncertainty is stated.

Hint

Use sinθ = nλ/d; check the argument is at most 1, then use inverse sine in degrees.

Worked solution

nλ/d = 2 × 500 × 600 / 10⁶.
θ = sin⁻¹(nλ/d), in degrees.
Answer: 36.9 ° (3 significant figures).

Another question

Question type: Mixed practice

Report a problem

Use the diffraction grating equation

A grating has 500 lines per mm, so slit spacing d = 1/(500 × 1000) = 2.00 × 10⁻⁶ m. For wavelength 600 nm and first order, sin θ = λ/d = 0.300, giving θ = 17.5°. The angle is measured from the straight-through normal.

Line density and slit spacing are reciprocals. Convert lines per mm to lines per metre before finding spacing. An order requires |nλ/d| ≤ 1; a value above 1 is physically unavailable, not an inverse-sine calculator error.

Practise wavelength and interference

Convert the line density

Multiply lines per mm by 1000 to obtain lines per m. Slit spacing d is the reciprocal of that density. Convert nm to m before using d sinθ = nλ.

Use the normal-incidence equation

θ is the angle between a diffracted principal maximum and the straight-through direction. n is an integer order. Use sine and inverse sine in degrees for these questions.

Check the order limit

The sine cannot exceed 1. These order-limit questions expressly require an angle strictly below 90°, so nλ/d must be less than 1. Equality is the grazing limit and is excluded here. Other questions may state a different treatment of the 90° boundary.

A-level relevance

AQA 7408: 3.3.2.2 (selected); OCR A H556: 4.4.3(g)(ii) (selected). Tasks cover the selected skills listed above.

AQA specification · OCR A specification