Suppose a small light source is placed at the center of two transparent spheres.

Question

Suppose a small light source is placed at the center of two transparent spheres. One sphere has a radius, R, and the other a radius, 2R. L lumens of light leave the light source and travel outward toward the spheres.

A) How does the illuminance (the lumens passing through each square meter of surface) at the inner sphere compare to the illuminance at the outer sphere, assuming no light absorption? Try to solve this problem by thinking about the following:
How much of the light passes through the first sphere? How much passes through the second sphere? How do the surface areas of the two spheres compare?

B) Since most light bulbs that you use are not true point sources of light, how do you think the answer to Question 1 would change if a typical light bulb were used?

Explanation / Answer

A) Smaller sphere = A
Larger sphere = B

Intensity is power per unit area,

so I of A is: P/4pi*r^2

and I of B is P/16pi*r^2.

The intensity at B is 1/4 of the intensity at A.

Also A= 4pi*r^2; B= 16pi*r^2. The surface area of B is the 4 times the surface area of A.

Intensity will change based on the square of the radius

B) Because a light bulb is not a point source, the intensity decrease would not be as uniform as it is in the above figure. Instead, if you visualize the light bulb as being broken up into many point light sources, each other will have its own spheres around in which intensity decreases. Because of this, the answer to question one would be difficult to calculate because you would have to take into account an infinite number of point sources within the lightbulb.

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