Math Is Fun Forum

MathNooblet

Guest

Help with variation =S

Hello, Grateful if someone could help me with some easy math...Easy for you that is!

The intensity of light on a screen varies inversely as the square of the distance between the screen and the light source.
If a screen is illuminated by light from a source which is 20m from it, where must the light be placed if the screen is to receive 5 times the illumination?

The amount of heat recieved by a body varaies inversely as the square of the distance of the body from the heat source. If the distance from the source is decreased by 60%, what effect does this have on the heat received.

Would be happy if you showed me how you came to the conclusion.

thanks.

James

fgarb

Member

Registered: 2006-03-03

Posts: 89

Re: Help with variation =S

Intensity represents the number of particles passing through some area in a given amount of time - in your case you're talking about light "particles" coming from a lamp. Let's say you know how many particles there are coming out of your lamp per second. You should also assume these particles fly out uniformly in all directions - this wouldn't make sense for a flashlight, say. You should then be able to answer questions like: "If I put a screen 20m away, how many particles will hit every square centimeter of it per second?"

One way to think about it is in terms of spheres. Assuming no particles are created or destroyed on the way out, at radius 20m the initial particles will be spread out over an area of 4*pi*20^2 - just the surface area of a sphere at your radius. So because the sphere has an area proportional to the square of its radius, the light particles become more diffuse as the square of the distance they travel outwards. And since the energy carried is proportional to the number of particles carrying it, you can say the same thing about the heat energy they deliver.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help with variation =S

square root of 5 is 2.236 I think, so divide 20 meters by 2.236 and get between 8 and 9 meters I guess.

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