1. 1
   A diffraction grating with 600 lines per millimetre is illuminated at normal incidence by a green laser of wavelength 532 nm. A set of sharp, bright spots is seen on a large curved screen placed around the grating.

   (a)

   At what angle to the straight-through direction is the first-order maximum observed?

   [1 mark]

   • A17.7°
   • B71.4°
   • C39.7°
   • D18.6°

   (b)

   What is the highest order of maximum that can be observed?

   [1 mark]

   • A2
   • B3
   • C4
   • D7

   (c)

   Explain why the maxima produced by the grating are much sharper and brighter than the fringes produced by a double slit with the same slit separation.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A waterproof lamp is fixed to the wall of a swimming pool, below the water surface. Water has a refractive index of 1.33 and air has a refractive index of 1.00. Light from the lamp travels up to the flat water surface, where some of it passes into the air.

   (a)

   What is the critical angle for light travelling from the water to the air?

   [1 mark]

   • A36.9°
   • B41.2°
   • C48.8°
   • D90.0°

   (b)

   As light passes from the water into the air, which changes occur?

   [1 mark]

   • ASpeed and wavelength both increase; frequency is unchanged
   • BSpeed increases, wavelength decreases; frequency is unchanged
   • CSpeed, wavelength and frequency all increase
   • DSpeed and frequency increase; wavelength is unchanged

   (c)

   A ray from the lamp meets the water surface at an angle of incidence of 35°. Calculate the angle of refraction in the air.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A laser of wavelength 650 nm illuminates two parallel slits. Each slit has a width of 0.080 mm and the centres of the slits are 0.40 mm apart. A screen is 3.0 m from the slits. The student sees equally spaced bright fringes, but they are not all equally bright: their brightness falls away on either side of the centre, and at certain positions an expected bright fringe is missing.

   (a)

   Determine the distance on the screen from the centre of the pattern to the first minimum of the single-slit diffraction envelope.

   [3 marks]

   (b)

   Deduce the number of bright interference fringes within the central maximum of the diffraction envelope, and explain why some expected bright fringes are missing.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two friends are talking on the far side of an open doorway 0.90 m wide. A third person stands in the next room, beside the wall and out of the line of sight through the doorway. He can hear the conversation but cannot see the two friends, and he notices that the deep voice of one friend is heard more clearly than the high-pitched voice of the other. Take the speed of sound in air as 340 m s⁻¹, a typical frequency of the deep voice as 200 Hz and of the high-pitched voice as 4000 Hz.

   (a)

   Explain, using diffraction, why the third person can hear the conversation but cannot see the two friends.

   [6 marks]

   (b)

   Discuss why the deep voice is heard more clearly than the high-pitched voice, and evaluate whether diffraction alone accounts for the listener hearing any sound at all.

   [6 marks]

   Total for question 4: 12 marks

End of questions