Chapter 24, Problem 3P

To determine

The wavelength and frequency of the light

Answer to Problem 3P

The wavelength is $6.24\times {10}^{-7}m$ .

The frequency is $4.81\times {10}^{14}Hz$ .

Explanation of Solution

Given info:

Distance between the slit, $d=0.048 mm$

Distance of the screen, $D=5.00m$

Distance between thepatterns, $x=6.5cm$

Formula used:

Distance between fringes is equal to product of wavelength and distance of screen from slits over distance between slits:

  $x=\frac{\lambda \times D}{d}$

Here, $\lambda$ is the wavelength.

Calculation:

Rearrange the formula, $x=\frac{\lambda \times D}{d}$ . So, $\lambda =\frac{x\times d}{D}$

Substitute the values in formula to calculate wavelength:

  $\lambda =\frac{6.5cm\times 0.048mm}{5.00m}=6.24\times {10}^{-7}m$

Now, calculate the frequency:

  $\text{v=}\frac{\text{c}}{\text{λ}}$

Speed of light, $c=3.00\times {10}^{8}m/s$

  $\lambda =6.24\times {10}^{-7}m$

Substitute all these values:

  $v=\frac{\text{3}{\text{.00×10}}^{\text{8}}\text{m/s}}{\text{6}\text{.24×}{\text{10}}^{\text{-7}}\text{m}}\text{=4}{\text{.81×10}}^{\text{14}}\text{Hz}$

Conclusion: The required wavelength is $6.24\times {10}^{-7}m$ and required frequency is $4.81\times {10}^{14}Hz$ .