Question

The 488 nm line from an argon ion laser is Doppler broadened to 2.7×109 Hz. Given that the laser’s mirrors are 1 m apart, determine the number of longitudinal modes within the gain bandwidth of the 488 nm line. Assume that the index of refraction of the gas is 1

Answer 1

Answer:

The number of longitudinal modes within the gain bandwidth is 18.

Explanation:

Given that,

Wavelength = 488 nm

Frequency $f=2.7\times10^{9}\ Hz$

Distance = 1 m

Index of refraction of the gas = 1

We need to calculate the number of longitudinal modes within the gain bandwidth

Using formula of number of longitudinal modes

$N=\dfrac{f\times 2\times\mu\times l}{c}$

Where, f = Doppler frequency

c = speed of light

l= separation

Put the value into the formula

$N=\dfrac{2.7\times10^{9}\times\times2\times1\times1}{3\times10^{8}}$

$N=18$

Hence, The number of longitudinal modes within the gain bandwidth is 18.