Until now it was assumed that the index of refraction (n) is constant along the optical cavity.

This assumption means that the length of the active medium is equal to the length of the optical cavity.

There are lasers in which the mirrors are not at the ends of the active medium, so L₁ is not equal to the length of the cavity (L).
In such case each section of the cavity is calculated separately, with its own index of refraction:

The length of the optical cavity of a Nd-YAG laser is 30 [cm].

The length of the laser rod which makes the active medium is 10 [cm].

The index of refraction of the laser rod is 1.823.

The rest of the cavity is air which have an index of refraction of 1.0.

Calculate the difference in frequencies between adjacent modes.