Superposition: (2) a diffraction grating.

The idea

A diffraction grating has many equally spaced parallel slits, with the grating spacing d equal to the reciprocal of the number of lines per metre. When monochromatic light passes through the grating, sharp maxima occur at angles θ given by d sin θ = nλ, where n is the order of the maximum. The zeroth-order maximum is at θ = 0°, and higher orders appear symmetrically on both sides. To determine wavelength, the angle θ for a chosen order is measured, often by finding the positions of the maxima on a screen or using a spectrometer, and λ = d sin θ / n. For example, with 300 lines per millimetre, d = 1 / (300 × 10³ m⁻¹) = 3.33 × 10⁻⁶ m; if the first-order maximum is at 10.0°, then λ = 3.33 × 10⁻⁶ m × sin 10.0° = 5.79 × 10⁻⁷ m. The many slits make the maxima very sharp, so angles can be measured precisely.

What earns the marks

• States that the grating spacing d equals the reciprocal of the number of lines per metre.
• Uses d sin θ = nλ, identifying n as the order of the maximum.
• Measures the angle θ for a chosen order, for example by locating the first-order maximum on a screen or with a spectrometer.
• Converts lines per millimetre to lines per metre and then to d in metres before calculating.
• Explains that the large number of slits produces sharp, bright maxima, improving precision.
• Recognises that the zeroth-order maximum is at θ = 0° and higher orders appear symmetrically.

Common mistakes and how to put them right

• Using d as the number of lines per metre rather than its reciprocal.

  Put it right by calculating d = 1 / N, where N is lines per metre.

• Forgetting to convert lines per millimetre to lines per metre.

  Put it right: Multiply by 10³ before taking the reciprocal.

• Using the angle in degrees directly in a calculator set to radians, or vice versa.

  Put it right by checking the calculator mode matches the angle unit.

• Confusing the order n with the number of slits.

  Put it right: n is the order of the maximum, an integer such as 1, 2 or 3.

Exam tips

• Write d = 1 / N and convert N to lines per metre before substituting into d sin θ = nλ.
• Measure the angle to the first-order maximum on both sides and average to reduce alignment error.
• Check that sin θ ≤ 1; if the calculated value exceeds 1, that order does not exist for the given wavelength.
• Quote the wavelength in metres or nanometres with a consistent unit and sensible significant figures.