# Illuminance and distance

Hello,

We had a lab in physics about the relationship between illuminance and distance. Our teacher gave use data so we make a graph of them. E is the illuminance in Lux and d is the distance in cm. (d,E) (50cm, 94 lux) (60cm, 64 lux) (70 cm, 49 lux) (80cm, 40 lux) (90 cm, 32 lux) (100cm, 26 lux)
It the graph, when I connect the points it give me an inverse proportion. My objective is to find an equation.

What I first tried is to find an equation directly from this graph but after searching on the internet I found this formula : E=I/d^2 and this explanation : intensity is inversely proportional to the square of the distance from the source. I do not understand, in my graph d is my abscissa not d^2 . I do not understand how we can use d^2 instead of d.

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## Answers and Replies

CWatters
Science Advisor
Homework Helper
Gold Member
Are you familiar with the equation for a straight line? Compare the standard equation for a straight line...

y = mx + c

with your equation which I have rewritten slightly..

E = I(1/d2) + 0

Then replot your data suitably modified so you get a straight line. Come back if you get stuck.

PS: It's not d2 you use.

Are you familiar with the equation for a straight line? Compare the standard equation for a straight line...

y = mx + c

with your equation which I have rewritten slightly..

E = I(1/d2) + 0

Then replot your data suitably modified so you get a straight line. Come back if you get stuck.

PS: It's not d2 you use.

E = I(1/d2) + 0

my question why is the equation not E=I(1/d)

where do the 2 come from

CWatters
Science Advisor
Homework Helper
Gold Member
Imagine a point source of light surrounded by a spherical glass surface of radius d. The light from the source spreads out uniformly in all directions and passes through the sphere. The "density" of the light (aka illuminance) passing through the glass will be...

The total amount of light emitted / Surface area of the sphere

In other words the bigger the sphere the less light will pass through each square meter.

What is the equation for the surface area of a sphere?