Chapter 22, Problem 17P

To determine

Number of wavelengths found within the laser pulse.

Answer to Problem 17P

The answer is $9040$ wavelengths,$3.54\times {10}^{-15}s$.

Explanation of Solution

Given info:

Wavelength, $\lambda =1062nm=1062\times {10}^{9}m$

Factor, $c=3.00\times {10}^{8}m/s$

Pulse lasts for time, $t=32pi\cos econds=32\times {10}^{12}s$

Formula used:

Formula to calculate the number of wavelengths: $N=\frac{\left(c\Delta t\right)}{\lambda }$

Where,

  $\Delta t$is time

  $\lambda$is wavelength

  $c$is a factor

Calculation:

Substitute the given values in formula, $N=\frac{\left(c\Delta t\right)}{\lambda }$

  $N=\frac{\left(3.0\times {10}^{8}m/s\right)\left(32\times {10}^{-12}s\right)}{1062\times {10}^{-9}m}=9040$ wavelengths.

The calculation for the timing of pulse that needs to be to fit only one wavelength:

It is known that: $t=\frac{\lambda }{c}$where, $t$ is time,$\lambda$is wavelength and $c$ is a factor. Now, by using this,

  $t=\frac{\left(1062\times {10}^{-9}m\right)}{\left(3.00\times {10}^{8}m/s\right)}=3.54\times {10}^{-15}s$

Conclusion: The required values are calculated.