| Date | May 2017 | Marks available | 3 | Reference code | 17M.3.SL.TZ2.10 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Determine | Question number | 10 | Adapted from | N/A |
Question
The graphs show the variation with time of the intensity of a signal that is being transmitted through an optic fibre. Graph 1 shows the input signal to the fibre and Graph 2 shows the output signal from the fibre. The scales of both graphs are identical.
The diagram shows a ray of light in air that enters the core of an optic fibre.
The ray makes an angle A with the normal at the air–core boundary. The refractive index of the core is 1.52 and that of the cladding is 1.48.
Determine the largest angle A for which the light ray will stay within the core of the fibre.
Identify the features of the output signal that indicate the presence of attenuation and dispersion.
The length of the optic fibre is 5.1 km. The input power of the signal is 320 mW. The output power is 77 mW. Calculate the attenuation per unit length of the fibre in dB\(\,\)km–1.
Markscheme
calculation of critical angle at core–cladding boundary «\(1.52 \times \sin {\theta _{\text{C}}} = 1.48\)» θC = 76.8º
refraction angle at air–core boundary 90º – 76.8º = 13.2º
«\(1.52 \times \sin 13.2^\circ = \;\sin A\)» A = 20.3º
Allow ECF from MP1 to MP2 to MP3.
[3 marks]
attenuation: output signal has smaller area
dispersion: output signal is wider than input signal
OWTTE
OWTTE
[2 marks]
attenuation = «\(10\log \frac{I}{{{I_0}}} = 10\log \frac{{77}}{{320}} = \)» «–» 6.2 «dB»
\(\frac{{ - 6.2}}{{5.1}}\) = «–» 1.2 «dB\(\,\)km–1»
Allow intensity ratio to be inverted.
Allow ECF from MP1 to MP2.
[2 marks]
