How Can I Calculate the Number of Photons in a Laser Cavity?

[Vegeta2019]

Homework Statement

The laser cavity is formed by two mirrors separated by 15 cm. One of the mirrors has an ultra-high reflectivity and the output mirror has the much lower reflectivity of 99.5 %. How many photons are there in the cavity?[/B]

The power of the laser is 1mW and the wavelength is 600nm

Homework Equations

E= hc/λ and N=P/E Hence N = Pλ/hc

Power out = Power in x (1 - reflectivity) ... Not sure about this formula

The Attempt at a Solution

I have different views to what is happening as I think the question is vague. So I only have worked out certain elements.

At full power N = Pλ/hc ... N=3.01x10¹⁵

We could work out the time inside the cavity t = 30x10^-2 /3x10⁸ which gives 1 nano second... Not sure if this is relevant to the question.

Using the formula Power out = Power in x (1 - reflectivity) gives a power of 1x10^-3 x(1 -0.05)
=9.5x10^-4

Using this new power N = Pλ/hc... N= 2.86x10¹⁵ photons/s

Would I then do 3.01x10¹⁵ - 2.86x10¹⁵ = 1.6x10¹⁴ ??

Not sure if this is correct. Is the time element I tried supposed to be used?

 

[DrClaude]

I would approach the problem this way: start by calculating the number of photons escaping the cavity per unit time, then figure out how many photons per unit time need to be hitting the semi-reflecting mirror for the calculated output, then figure out how many photons must be inside the cavity to get this hit rate on the mirror.

 

[Vegeta2019]

So If I work our the photons escaping the cavity per uni time this would look like

Photons escaping = 3.01x10¹⁵ / 1x10^-9 =3.01x10²⁴ since the time the spend in the cavity is 1 nano second??
From my attempt the number of photons needed to hit the semi reflecting mirror is N= 2.86x10^15 photons/s due to the 0.5% loss?

So it would be 3.01x10²⁴ - 2.86x10¹⁵ = 3x10²⁴

Still not sure if I am doing this correct.