Functions, 2ADV EQ-Bank 8

The intensity of light \((I)\), measured in lux, from a lamp varies inversely with the square of the distance from the lamp \((d)\), measured in metres.

At a distance of 2.2 metres from the lamp, the light intensity is 400 lux.

What is the light intensity at a distance of 5.0 metres from the lamp? (2 marks)

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\(77.44\ \text{lux}\)

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\(I \propto \dfrac{k}{d^2} \ \Rightarrow \ I=\dfrac{k}{d^2}\)

\(\text{Find k given} \ \ I=400 \ \ \text {when} \ \ d=2.2:\)

\(400=\dfrac{k}{2.2^2} \ \Rightarrow \ k=1936\)

\(\text{Find \(I\) when \(\ d=5\):}\)

\(I=\dfrac{1936}{5.0^2}=77.44\ \text{lux}\)