1. 1
   An optical fibre has a glass core of refractive index 1.50 surrounded by a cladding of refractive index 1.40. Monochromatic light is sent into one end of the fibre and travels along the core by striking the core–cladding boundary many times.

   (a)

   What is the critical angle at the core–cladding boundary?

   [1 mark]

   • A21.0°
   • B41.8°
   • C69.0°
   • D90.0°

   (b)

   What is the speed of the light in the core?

   [1 mark]

   • A2.00 × 10⁸ m s⁻¹
   • B2.14 × 10⁸ m s⁻¹
   • C3.00 × 10⁸ m s⁻¹
   • D4.50 × 10⁸ m s⁻¹

   (c)

   A ray in the core meets the core–cladding boundary at an angle of incidence of 75°. Explain what happens to this ray.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a Young's double-slit experiment, a red laser of wavelength 633 nm illuminates two narrow slits whose centres are 0.25 mm apart. A pattern of equally spaced bright and dark fringes forms on a screen 2.4 m from the slits.

   (a)

   What is the separation of adjacent bright fringes on the screen?

   [1 mark]

   • A6.1 × 10⁻⁶ m
   • B6.1 × 10⁻³ m
   • C3.0 × 10⁻³ m
   • D9.5 × 10² m

   (b)

   At a point X on the screen, the path difference between the waves arriving from the two slits is 1.90 μm. What is observed at X?

   [1 mark]

   • AA dark fringe, because the waves arrive in antiphase
   • BHalf the maximum brightness, because the waves are a quarter-cycle out of phase
   • CThe central bright fringe, because the path difference is a whole number of wavelengths
   • DA bright fringe, because the waves arrive in phase

   (c)

   Explain why placing a separate lamp behind each slit, instead of using one laser, would not produce an observable fringe pattern.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a ripple tank, plane water waves of frequency 12 Hz travel through deep water, where their wavelength is 2.0 cm. They cross a straight boundary into shallow water. In the deep water the wavefronts make an angle of 50° with the boundary; in the shallow water they make an angle of 32° with the boundary. The waves then continue through the shallow water towards a barrier containing a gap. With a gap of width 6.0 cm the waves emerge almost straight with only slight spreading at the edges; when the gap is narrowed to 1.5 cm the waves emerge as almost semicircular wavefronts.

   (a)

   Determine the speed of the waves in the shallow water.

   [3 marks]

   (b)

   Explain the difference between the two diffraction patterns and predict, with a reason, how the pattern for the 1.5 cm gap would change if the frequency were increased to 24 Hz.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two loudspeakers 1.5 m apart are connected to the same signal generator and emit sound of frequency 680 Hz in phase. The speed of sound in air is 340 m s⁻¹. A student walks slowly across the room in front of the loudspeakers and hears the sound alternate between loud and quiet. At point Q she is 5.00 m from one loudspeaker and 6.00 m from the other, and the sound is loud. At point P she is 4.00 m from one loudspeaker and 4.75 m from the other, and the sound is quiet but not completely silent.

   (a)

   Explain, using the principle of superposition, why the sound is loud at Q and quiet at P.

   [6 marks]

   (b)

   Discuss why P is quiet but not silent, and evaluate whether an arrangement like this could be used to make one area of a room silent for speech or music.

   [6 marks]

   Total for question 4: 12 marks

End of questions