Question

A carbon dioxide laser is an infrared laser. A CO2 laser with a cavity length of 53.00 cm oscillates in the m = 100,000 mode. What are the wavelength and frequency of the laser beam?

Short answer

The wavelength of the laser beam is $1.06\times {10}^{-5}m$.

The frequency of the laser beam is$2.83\times {10}^{13}Hz$.

Step-by-step solution

Given information

The length of the cavity is $L=53.00cm=0.53m$

Mode$m=100,000$

The wavelength of the Laser beam

A laser light forms a standing wave inside the cavity.

The wavelength of the laser beam is given by $\lambda =\frac{2L}{m}$.

Substitute the given values

$$\begin{gathered} \lambda =\frac{2\times 0.53}{100000} \\ =1.06\times {10}^{-5}m \end{gathered}$$

Therefore, the wavelength of the laser beam is$1.06\times {10}^{-5}m$.

Frequency of the laser beam

The frequency of the laser beam is

$$\begin{gathered} f=\frac{c}{\lambda } \\ =\frac{3\times {10}^8}{1.06\times {10}^{-5}} \\ =2.83\times {10}^{13}Hz \end{gathered}$$

Therefore, the frequency of the laser beam is$2.83\times {10}^{13}Hz$.