CAIE A-Level Physics Radians, Exponentials and Logarithms

Practise using radians, small-angle approximations, exponential and logarithmic laws, and transformed plots to analyse exponential or power-law relationships.

Exam points

use radians, exponentials and logarithms in physical calculations
recognise logarithmic forms and use logarithmic plots to test exponential or power-law variation
calculate or interpret quantities from a logarithmic relationship, including gradients and intercepts

[Maximum number: 3]

Optic fibres are used for the transmission of data.

The attenuation per unit length of the signal in the fibre is $0.40 \mathrm{~dB} \mathrm{~km}^{-1}$ . The input power is 1.5 mW and the output power is 0.060 mW .

Calculate the length of the fibre.
length = km

attenuation $=10 \log \left(\mathrm{P}_{2} / \mathrm{P}_{1}\right)$

C1

$0.40 \times L=10 \log (1.5 / 0.06)$ $0.40 \times L=13.979$

C1

$L=35 \mathrm{~km}$

A1

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M.5-A Level radians, exponentials and logarithms question 1