Higher November 2019 Unit 1 Q11
11. The illuminance of light, \(I\), from a lamp depends on the distance, \(d\), from the lamp.
The unit used to measure the illuminance of light is the lux.
It is known that \(I\) is inversely proportional to the square of \(d\).
Carys has a desk lamp in her room.
For her lamp, Carys measures the illuminance, \(I\), to be 5 lux when the distance, \(d\), is 2 m.
What is the illuminance of light from this lamp at a distance of 0·5 m? [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(I \;\alpha\; 1 / d^{\,2}\) OR \(I = k / d^{\,2}\) or equivalent | B1 | Allow \(I \;\alpha\; k / d^{\,2}\) |
| \(5 = k / 2^2\) OR \(k = 20\) | M1 | M1 implies B1. F.T. (for possible B0 M2 A0) for use of \(I \;\alpha\; d^{\,2}\) or \(I \;\alpha\; 1 / d^{\,n}\) with \(n > 0\) and \(n \ne 2\). |
| \(I = 20 / d^{\,2}\) OR \(I = 20 / 0{\cdot}5^{\,2}\) or equivalent | M1 | |
| \(I = 80\) (lux) | A1 | CAO. Use of \(I \;\alpha\; 1 / d\) , leading to \(I = 10 / d\) (or an answer of \(I = 20\) (lux)) is awarded B0 FT M2 A0. Use of \(I \;\alpha\; d^{\,2}\), leading to \(I = 1{\cdot}25\, d^{\,2}\) (or an answer of \(I = 0{\cdot}3125\) (lux)) is awarded B0 FT M2 A0. Use of \(I \;\alpha\; 1 / \sqrt{d}\), leading to \(I = 5\sqrt{2} / \sqrt{d}\), (or an answer of \(I = 10\) (lux)) is awarded B0 FT M2 A0. |