# Maths

#1
The inverse law states that the intensity of illumination is inversely proportional to the square of the distance from the point source.

I  _1_
d2

A student carried out an investigation, measuring a set of intensity readings ( I ) on a light meter at various distances ( d) from a point source of light. The results are shown in the table below :

Intensity ( I ) W/m2 15 48 116 249 442 761
distance ( d ) cm 114 64 41 28 21 16
1/distance2 ( 1/d2 ) cm-2
1/distance2 ( 1/d2 ) cm-2 X10-5

9a) Plot a graph of intensity ( y-axis ) against distance ( x-axis ).What
does this graph indicate ?

9.b) Plot another graph of intensity (y-axis) against 1/ d2 (x-axis)

9c) Using the results , develop a relationship between ( I ) and ( d )
and hence prove that the inverse law holds. Remember I x d2 = Constant

9 d) Find the gradient of the graph in (b).

9e) Find the gradient of the graph in a) when d = 45 cm by drawing a tangent to the line and drawing a tangent to the line.
0
5 years ago
#2
(Original post by mark000)
The inverse law states that the intensity of illumination is inversely proportional to the square of the distance from the point source.

I  _1_
d2

A student carried out an investigation, measuring a set of intensity readings ( I ) on a light meter at various distances ( d) from a point source of light. The results are shown in the table below :

Intensity ( I ) W/m2 15 48 116 249 442 761
distance ( d ) cm 114 64 41 28 21 16
1/distance2 ( 1/d2 ) cm-2
1/distance2 ( 1/d2 ) cm-2 X10-5

9a) Plot a graph of intensity ( y-axis ) against distance ( x-axis ).What
does this graph indicate ?

9.b) Plot another graph of intensity (y-axis) against 1/ d2 (x-axis)

9c) Using the results , develop a relationship between ( I ) and ( d )
and hence prove that the inverse law holds. Remember I x d2 = Constant

9 d) Find the gradient of the graph in (b).

9e) Find the gradient of the graph in a) when d = 45 cm by drawing a tangent to the line and drawing a tangent to the line.
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