Moving a lamp when illumination varies inversely as the square of distance
Moving a lamp when illumination varies inversely as the square of distance
IP 2
8 marks
The illumination \(I\) units on a desk is inversely proportional to the square of the distance \(d\) m between the desk and a lamp. When \(d=2\), \(I=45\).
- Find the illumination when the lamp is \(3\) m from the desk.[2]
- The lamp is moved so that the illumination is doubled. Find the factor by which the distance has been multiplied, leaving your answer in exact form.[3]
- Show that increasing the distance by \(10\%\) reduces the illumination by about \(17\%\), and explain why the reduction is not \(20\%\).[3]
Solution:
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Answer:(a) \(20\) units (b) \(\dfrac{\sqrt{2}}{2}\) (c) \(1-\dfrac{1}{1.21}\approx17\%\); \(I\) is divided by \(1.21\), not multiplied by \(0.8\)
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