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Question 23M.3.HL.TZ2.14

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Date May 2023 Marks available [Maximum mark: 6] Reference code 23M.3.HL.TZ2.14
Level HL Paper 3 Time zone TZ2
Command term Calculate, Deduce, Discuss Question number 14 Adapted from N/A
14.
[Maximum mark: 6]
23M.3.HL.TZ2.14

Signals in an optic fibre require amplification when intensity levels in the fibre have fallen to 1.5 % of the original signal. A light signal of initial intensity I0 is sent down the optic fibre.

(a)

The fibre has an attenuation per unit length of 0.30 dB km−1. Deduce that the length of the fibre is approximately 60 km before the signal requires amplification.

[2]

Markscheme

attenuation = 10 log10(0.015) OR = −18.2 ✓


length = -18.2-0.3

OR

60.8 «km» ✓

 

Allow ECF from MP1

Ignore signs

A signal is sent down a 27 km step-index fibre and received according to the intensity–time graph below.

(b)

Calculate the refractive index of the fibre.

[2]

Markscheme

Δt = 14 × 10−5 s ✓

«27×10314×10-5 = 3×108n» : n = 1.56 ✓

 

Award MP1 if Δt = 14 × 10−5 s is seen anywhere

Allow ECF for MP2, if candidates use Δt = 18 – 3 OR Δt = 20 – 4, accepting n = 1.67 or = 1.78

(c)

Discuss how using a graded-index fibre could reduce waveguide dispersion.

[2]

Markscheme

refractive index of fibre is less at the edges ✓

reduces time taken for the longer path signals ✓

 

OWTTE