How many photons are there in a 1 m long He-Ne laser beam?

[manaXmizery]

Homework Statement

A He-Ne laser emits red light of the wave length lambda =632.8 nm with a beam diameter of 2.0 mm and a power output of 1.0 mW. (a) What is the intensity of this laser beam? (b) What is the magnitude of the momentum of each photon? (c) How many photons does this laser emit each second? (d) How many photons are there in the 1 m long laser beam?

Homework Equations

I = P/A

N = P/E

P= h/lambda

The Attempt at a Solution

(a) I = P/A

Hence , I = 0.001 / 4*pi*(0.001) = 79.577 W/m

(b) P = h / lambda = 1.047 *10^-27 kg.m/s

(c) E = h*lambda/c = 1.398 * 10^-48 J

N = P/E = 7.15 * 10^44 photons / second

(d) I am not sure if the 1 m here is referring to the wavelength or the length - can anyone explain it to me ? Thanks in advance.

 

[blue_leaf77]

(d) I am not sure if the 1 m here is referring to the wavelength or the length - can anyone explain it to me ?

In (c), you have calculated the amount of photons traversing any perpendicular plane along the propagation direction. Fix a plane somewhere in the beam, in one second there are N (whose value you have calculated) photons going in. Then place a second plane 1 m apart from the first one. With the knowledge of the time needed by a beam of light to travel 1 m distance, you should be able to calculate the amount of photons traversing into the first plane (or equivalently traversing out of the second plane) during the same amount of time. This will be equal to the number of photons contained in a 1 m beam.