Rami Arieli: "The Laser Adventure" Chapter 4 Section 1, page 3

 Conditions for Standing Waves

In order to create a standing wave, the wave must start with the same phase at the mirror.

Thus, the optical path from one mirror to the other and back must be an integer multiplication of the wavelength.

Since the Length between the mirrors is constant (L), the suitable wavelengths, which create standing waves, must fulfill the condition:

lm = 2L/m
L = Length of the optical cavity.

m = Number of the mode, which is equal to the number of half wavelengths inside the optical cavity. The first mode contains half a wavelength, the second mode 2 halves (one) wavelength.

lm = Wavelength of mode m inside the laser cavity.

 The wavelength of the laser mode (lm) is measured inside the active medium.

Wavelength in matter (lm) is equal to:

lm = l0/n
l0 = Wavelength of light in vacuum.
n = Index of refraction of the active medium.
c = Velocity of light in vacuum. Since:
c = l0n = nlmnm
The frequency of the longitudinal mode is:
Inserting lm into the last equation:
The mathematical expression in parenthesis is the first mode of oscillation available for this optical cavity:

This mode is called basic longitudinal mode, and it has the basic frequency of the optical cavity.