# Wavelength of a laser within an optical cavity

• Taylor_1989
In summary, the conversation discusses the problem statement and variables for question 5 of a homework assignment. The equations [1] and [2] are used to calculate the cavity length and number of modes. The speaker is having trouble with question 5 and believes their cavity length may be incorrect, but is unsure why. They provide their working and ask for advice. After realizing their mistake, they correct their answer for the path length to be 0.9m.
Taylor_1989
1. The problem statement, all variables and given/known date

## Homework Equations

$$\delta v=\frac{c}{2nL} \:[1]$$
$$N=\frac{\Delta v}{\delta v}=\frac{2nL\Delta v}{c} \:[2]$$

## The Attempt at a Solution

I am having trouble with question 5, but have come to realize I think my cavity length is wrong but I can't see how.

Here my working for question 1

Assuming that the medium is in the middle at equal distance from each mirror, then I could assume that ##L=L_{m}+2x## so subsituiting this into equation 1.

$$\delta v=\frac{c}{2nL}=\frac{c}{2n(L_{m}+2x)}$$

by rearranging the equation for x

$$x=\left(\frac{c}{\delta \:v}\cdot \:\frac{1}{2n}-Lm\right)\cdot \frac{1}{2}$$

so subbing ##x=0.1## I make the cavity length ##L=L_{m}+2(0.1)=0.5m##.

Which seem to reasonable to me. But if I plug this length of the cavity into [2] and using the spectral range of ##3\times 10^{7}## I make the number of modes 0.3 which can't be correct.

So the reason I want to workout the number of modes is so I can verify the ##600nm## via the equation ##\lambda=2\times L_{c}/N##, which dose not give the 600nm so either my cavity is length is wrong or my understanding is wrong.

Any advice would be much appreciated.

#### Attachments

• optic1.png
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• optic2.png
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Taylor_1989 said:
δv=c2nL=c2n(Lm+2x)δv=c2nL=c2n(Lm+2x)​
\delta v=\frac{c}{2nL}=\frac{c}{2n(L_{m}+2x)}
Only Lm is at index n. Here you have the whole path at index n

Cutter Ketch said:
Only Lm is at index n. Here you have the whole path at index n

Yes I realized this after a while, and then re corrected my ans for the path length being 0.9m

## What is a laser's wavelength and how does it relate to an optical cavity?

A laser's wavelength is the distance between successive peaks of the electromagnetic wave that makes up the light. It is a crucial parameter in determining the properties of a laser, such as its color and energy. Within an optical cavity, the laser's wavelength is determined by the length of the cavity and the material it is made of.

## Why is the wavelength of a laser important in an optical cavity?

The wavelength of a laser is important in an optical cavity because it determines the resonant modes of the cavity. These resonant modes are essential in producing a stable and amplified laser beam. If the laser's wavelength is not matched to the cavity, the laser will not function properly.

## What factors can affect the wavelength of a laser within an optical cavity?

The wavelength of a laser within an optical cavity can be affected by several factors, including the material and construction of the cavity, the temperature and pressure of the environment, and the amount of energy being pumped into the laser. Changes in any of these factors can cause a shift in the laser's wavelength.

## How is the wavelength of a laser within an optical cavity measured?

The wavelength of a laser within an optical cavity can be measured using various techniques, such as interferometry, spectroscopy, or diffraction. These methods involve analyzing the interference patterns, emission spectra, or diffraction patterns of the laser beam to determine its precise wavelength.

## Can the wavelength of a laser within an optical cavity be tuned or controlled?

Yes, the wavelength of a laser within an optical cavity can be tuned or controlled by adjusting the length of the cavity or by changing the material it is made of. This allows for precise control over the laser's properties and can be useful in various applications, such as in telecommunications or scientific research.

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