9702/Oct Nov/11/2015/Q6

A light-meter measures the intensity I of the light incident on it. Theory suggests that I varies
inversely as the square of the distance d.

Which graph of the results supports this theory?

Solution:
Answer: C

Theory suggests that the intensity I varies as the inverse square of the distance d.

I α 1 / d²

I = k (1 / d²) = k / d²    where k is a constant

Consider the graph of I (on y-axis) against 1/d² (on x-axis).

Equation of a line: y = mx + x

Compare I = k (1 / d²) = k / d² with the equation y = mx + c:

y = I

x = 1 / d²

m = k

c = 0

So, if a graph of I against 1/d² is plotted, it should be a straight line with a positive gradient (the constant k is positive) and starting at the origin (y-intercept, c = 0 – that is, it intercepts the y-axis at y=0). [C is correct]

Options A and B both have the graph cutting an axis, which would not be the case for an inverse square law graph.

A graph of I against d² would be similar to a graph of y = 1 / x where y = I and x = d². Such a graph is a curve with a negative gradient and not touching the axes.

Type: graph y=1/x

at Google search to see to shape of the graph.

Reference: PYQ - Oct/Nov 2015 Paper 11 Q6