Diffraction and interference

Sample questions

Original practice questions written in the style of the exam.

1. Question 13 marks

   Laser light of wavelength $633\,\text{nm}$ is incident normally on a diffraction grating that has $500$ lines per millimetre.

   Calculate the angle between the central (zero-order) maximum and the second-order maximum.

   Mark scheme

   • $d = 1/(500 \times 10^{3}) = 2.0 \times 10^{-6}\,\text{m}$ (1)
   • $\sin\theta = n\lambda/d = 2 \times 633 \times 10^{-9}/2.0 \times 10^{-6} = 0.633$ (1)
   • $\theta = 39^\circ$ (1)
2. Question 23 marks

   Two loudspeakers are connected to the same signal generator and placed a short distance apart. A student walking along a line in front of them hears regions of loud and quiet sound.

   (a) Explain why the two sources are coherent.

   (b) Explain why a loud region is heard at a point where the path difference from the two speakers is one whole wavelength.

   Mark scheme

   • The speakers are driven by the same generator, so they have the same frequency and a constant phase difference (1)
   • A path difference of $\lambda$ means the waves arrive in phase (1)
   • They superpose constructively, giving maximum amplitude/loud sound (1)