Question

A laser pointer delivers an average power of 2 mW in a circular beam of 2 mm diameter. What is the average energy density in the beam?

a) 0.75E-6 J/cubic meter

b) 1.5E-6 J/cubic meter

c) 2.1E-6 J/cubic meter

d) 4.4E-6 J/cubic meter

e) 7.6E-6 J/cubic meter

Answer 1

Given the average power delivered by the laser P = 2mW and the diameter of the beam d = 2mm. So the radius of the beam r = 1mm. If A is the area of the beam, the intensity of the beam is given by,

$I = \frac{P}{A}=\frac{P}{\pi r^{2}}=\frac{2\times 10^{-3}}{\pi\times (1\times 10^{-3})^{2}}=636.62W/m^{2}$

The average energy density Uav is given by,

$U_{av} = \frac{I}{c}=\frac{636.62}{3\times 10^{8}}=2.1\times 10^{-6}J/m^{3}$

So the average energy density in the beam is 2.1 x 10^-6 J/m^3 or 2.1E-6 J/cubic meter.

Option (c) is the correct answer.