(g) transmission diffraction grating used to determine the wavelength of…

The idea

A transmission diffraction grating has many equally spaced parallel slits. Monochromatic light passing through the grating produces sharp maxima at angles given by d sin θ = nλ, where d is the grating spacing, n is the order and λ is the wavelength. To determine wavelength, measure the angle θ for a known order n and calculate λ = d sin θ / n. The grating spacing d equals 1 divided by the number of lines per metre. Because the maxima are sharp, the angle can be measured precisely, giving an accurate wavelength. A spectrometer or optical bench with a protractor measures the angle between the zero-order and nth-order maxima.

What earns the marks

• A transmission diffraction grating consists of many equally spaced parallel slits.
• Light passing through the grating produces sharp maxima at angles satisfying d sin θ = nλ.
• The grating spacing d is the reciprocal of the number of lines per metre.
• Wavelength is determined by measuring the angle θ for a known order n and using λ = d sin θ / n.
• The sharpness of the maxima allows precise angle measurement and therefore accurate wavelength determination.

Common mistakes and how to put them right

• Using the number of lines per millimetre directly as d instead of converting to metres and taking the reciprocal.

• Measuring the angle between adjacent orders rather than between the zero-order and the nth-order maximum.

• Forgetting to divide by n when calculating wavelength from d sin θ = nλ.

• Confusing the grating spacing d with the slit width of a double slit.

  Put it right: In a grating d is the distance between adjacent slits.

Exam tips

• Always convert lines per millimetre to lines per metre before calculating d = 1/N.
• Measure the angle from the zero-order maximum to the centre of the nth-order maximum, not between two non-zero orders.
• Use a large number of lines and a high order where possible to increase the angle and reduce percentage uncertainty in θ.