Physics Homework Help?

Question

Treat a firefly as an isotropic source of light. 5.33 m away from a firefly, you measure an intensity of 2.13×10-8 W/m2. What is the power output of this source? Convert your answer and enter it with units of uW (microwatts, where "micro-" = ×10−6). If this light were focused into a laser beam with a radius of 1.93 mm, what would be the intensity of light within the beam? Enter the units as W/m^2.

For the power, I was thinking I could use the formula I=P/(pi*r^2) and solve for P. When doing this I got 1.901 *10^-6. (This may be wrong but this was just my thinking.)

However, I am not sure where to go for the second part of the problem. I was thinking maybe the same direction? Any help is appreciated! 

Answer 1

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For the power you have the right idea but the wrong formula. The area to use is that of a SPHERE of radius r, not a circle. So

P = I*A = I*4πr²

I get 7.60e-6 W = 7.60 µW.

As a laser beam, the light is NOT isotropic, but is cast only over a CIRCLE of the radius given.

I = P / A = P / πr²

Using the new radius, I get I = 0.650 W/m²

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