How Does Illuminance Change With Distance in Physics Experiments?

[garet122]

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.

 

[CWatters]

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.

 

[garet122]

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]

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?

 

[Nickie]

Hello,

Thank you for sharing your findings from your physics lab. It is interesting to see the relationship between illuminance and distance and how it follows an inverse proportion. Let me explain the use of d^2 in the formula E=I/d^2.

The inverse square law states that the intensity of light decreases as the distance from the source increases. This means that as the distance (d) increases, the intensity (I) decreases. However, the decrease in intensity is not proportional to the distance, but to the square of the distance (d^2). This is why the formula uses d^2 instead of d.

In your experiment, you measured the illuminance (E) at different distances (d). By using the formula E=I/d^2, you can calculate the intensity (I) at each distance. This allows you to see the relationship between the two variables and how it follows an inverse proportion.

I hope this explanation helps you understand the use of d^2 in the formula. Keep up the good work in your physics studies!