The problem statement is: "A He-Ne laser operating in the TEM00 mode has a beam diameter of 2 mm at the output mirror and a wavefront radius of curvature of 5 m. If the input power is 2 mW, what is the output power?"
The equation used is Pout = Pin * (1 - R) * (1 - exp(-2 * L / w0^2)), where Pout is the output power, Pin is the input power, R is the reflectivity of the output mirror, L is the length of the cavity, and w0 is the beam waist radius.
The key assumptions are: the laser is operating in the TEM00 mode, the cavity is linear and stable, the beam diameter and wavefront radius of curvature are constant throughout the cavity, and there are no losses due to scattering or absorption.
The reflectivity is calculated using the Fresnel equations for reflection, where R = (n1 - n2)^2 / (n1 + n2)^2, where n1 and n2 are the refractive indices of the two materials that make up the mirror.
Solving this problem allows us to determine the output power of a He-Ne laser based on the input power and other parameters of the laser cavity. This is important for understanding and optimizing the performance of a laser system.