Question

A carbon-dioxide laser emits infrared light with a wavelength of 10.6 μm. What is the length of a tube that will oscillate in the m = 160000 mode? Imagine a pulse of light bouncing back and forth between the ends of the tube. How many round trips will the pulse make in each second?

Answer 1

Answer:

The length of a tube and number of rounds are 0.848 m and $1.77\times10^{8}\ trip\ per\ second$.

Explanation:

Given that,

Wavelength $\lambda= 10.6\mu m$

m = 160000

We need to calculate the length

Using formula of wavelength

Laser tube behave like closed pipe

$m\dfrac{\lambda}{2}=L$

$L=160000\times\dfrac{10.6\times10^{-6}}{2}$

$L=0.848\ m$

Distance traveled by pulse of light in one back and fourth trip

$d=2L$

$d=2\times0.848$

$d=1.696\ m$

We need to calculate the time

Using formula for time

$t = \dfrac{d}{c}$

$t=\dfrac{1.696}{3\times10^{8}}$

$t=5.653\times10^{-9}\ s$

We need to calculate the number of round

Using formula of number of round

$N=\dfrac{1}{t}$

$N= \dfrac{1}{5.653\times10^{-9}}$

$N=1.77\times10^{8}\ trip\ per\ second$

Hence, The length of a tube and number of rounds are 0.848 m and $1.77\times10^{8}\ trip\ per\ second$.