Question

A 0.50 mW laser produces a beam of light with a diameter of 1.6 mm . Part A What is the average intensity of this beam? Part B At what distance does a 130 W lightbulb have the same average intensity as that found for the laser beam in part (a)? (Assume that 5.0% of the bulb's power is converted to light.) Express your answer using two significant figures.

Answer 1

(a) Diameter, d = 1.6 mm = 1.6x10^-3 m

So, radius, r = d/2 = 8.0 x 10^-4 m.

Area, A = 4*pi*r^2 = 4*3.141*(8.0 x 10^-4)^2 = 8.04x10^-6 m^2

So, the average intensity of the beam, I = P/A = ( 0.50x10^-3) / (8.04x10^-6) = 62.19 W/m^2

(b) Suppose the requisite distance is R meter.

So its intensity, I = P/(4*pi*R^2) = (0.05*130) / (4*pi*R^2)

Now as per the condition –

(0.05*130) / (4*pi*R^2) = 62.19

=> 4*pi*R^2 = 0.1045

=> R^2 = 0.00832

=> R = 0.0912 m = 9.1 cm (two significant figures)