Diffraction grating practice

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

Practise

Identify an order

At a principal maximum, the path difference between waves from adjacent slits is 1350 nm for light of wavelength 450 nm. Find the integer diffraction order.

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

Hint

At a principal maximum, path difference = nλ.

Worked solution

n = 1350/450 = 3.

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