Question

A gas laser has a cavity length of 1/3 m and a single oscillation frequency of 9.0 x 1014 Hz. What is the cavity mode number?

Answer 1

Answer:

2 × 10⁶

Explanation:

Data provided in the question:

Cavity length, L = $\frac{1}{3}m$

Oscillation frequency, $f_m$ = 9.0 × 10¹⁴ Hz

Now,

we know,

$f_m=\frac{c}{\lambda_m}$

here,

c is the speed of light = 3 × 10⁸ m/s

$\lambda_m$ = Wavelength of mode m inside the laser cavity

m is the cavity mode number

Thus,

$9.0\times10^{14}=\frac{3\times10^8}{\lambda_m}$

or

$\lambda_m$ = $\frac{1}{3}$ × 10⁻⁶

Also,

$m\lambda_m = 2L$

Therefore,

m × $\frac{1}{3}$ × 10⁻⁶ = 2 × $\frac{1}{3}$

or

m = 2 × 10⁶