A HeNe laser produces light with a wavelength of 632.8nm. The neon atoms, which emit the light, are moving at a mean velocity of 406m/s?
a. What is the difference in the observed freq of light emitted from Ne atoms moving direction toward the exit mirror as opposed to those which are moving away from
the exit mirror?
b. If the cavity length is 40cm how many cavity modes will be observed in the output
spectrum? Use the freq calculated in a) as the width of the output spectral line).
To answer these questions, we need to understand the concepts of Doppler shift and cavity modes in the context of a HeNe laser.
a. The Doppler effect is the change in frequency or wavelength of a wave observed by an observer moving relative to the source of the wave. In the case of a moving source, such as the neon atoms in a HeNe laser, the observed frequency of light can be different depending on the direction of the atom's motion.
The formula for the Doppler shift in frequency is given by:
Δf/f = v/c
where Δf is the change in frequency, f is the original frequency, v is the velocity of the source, and c is the speed of light.
In this case, the neon atoms are moving at a mean velocity of 406 m/s. Since the neon atoms are emitting light, we can assume that the observed frequency for atoms moving towards the exit mirror will be higher than the frequency emitted by atoms moving away from the exit mirror.
Using the Doppler shift formula:
Δf/f = v/c
Δf = (v/c) * f
Substituting the given values:
Δf = (406 m/s / 3 x 10^8 m/s) * f
We are given the wavelength (λ) of the emitted light, which is 632.8 nm. We can use the formula: speed of light (c) = wavelength (λ) * frequency (f).
c = λ * f
Rearranging the formula, we can express the frequency as:
f = c / λ
Substituting the values:
f = (3 x 10^8 m/s) / (632.8 x 10^(-9) m)
Now we can calculate the difference in the observed frequency for atoms moving towards and away from the exit mirror:
Δf = (406 m/s / 3 x 10^8 m/s) * [(3 x 10^8 m/s) / (632.8 x 10^(-9) m)]
Simplifying the expression will give you the answer for part a.
b. In a laser cavity, the length determines the spacing between the allowed frequencies or cavity modes of the laser light. The cavity modes are determined by the round-trip path length of the laser in the cavity.
The formula for the cavity mode spacing is:
Δf_mode = c / 2L
where Δf_mode is the spacing between the cavity modes, c is the speed of light, and L is the cavity length.
Substituting the given values:
Δf_mode = (3 x 10^8 m/s) / (2 * 0.4 m)
Simplifying the expression will give you the answer for part b.