Q4E - University Physics with Modern Physics

Question

Light with a frequency of $\mathbf{5}\mathbf{.}\mathbf{80}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{Hz}$ travels in a block of glass that has an index of refraction of 1.52. What is the wavelength of the light (a) in vacuum and (b) in the glass?

Step-by-Step Solution

Answer

1. The wavelength of the light in vacuum is 517 nm .
2. The wavelength of the light in the glass is 340 nm.

Step 1: (a) Determination of The wavelength of the light in vacuum.

The expression for wavelength in air is,

${\lambda }_0=\frac{c}{f}$ 

Given, $\mathrm{f}=5.80\times {10}^{14}\mathrm{Hz}$ and $\mathrm{c}=3.00\times {10}^8\mathrm{m}/\mathrm{s}$. Substitute the values in above equation,

 $$\begin{gathered} {\mathrm{\lambda }}_0=\frac{3.00\times {10}^8\mathrm{m}/\mathrm{s}}{5.80\times {10}^{14}\mathrm{Hz}} \\ =517 nm \end{gathered}$$ 

Thus, the wavelength in vacuum is  517 nm.

Step 2: (b) Determination of the wavelength of light in glass.

The expression for wavelength in glass is,

$\lambda =\frac{{\lambda }_0}{n}$

  

Given n = 1.52.  Substitute the value in above equation,

 

$$\begin{gathered} \lambda =\frac{517 nm}{1.52} \\ =340 nm \end{gathered}$$

 

Thus, the wavelength in vacuum is 340 nm.