Q3E - University Physics with Modern Physics

Question

A beam of light has a wavelength of 650 nm in vacuum. (a) What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.47? (b) What is the wavelength of these waves in the liquid?

Step-by-Step Solution

Answer

1. The speed of the light in the given liquid is $2.04\times {10}^{8}m/s$ 
2. The wavelength of the waves in the liquid is 442 nm.

Step 1: (a) Determination of speed in liquid.

The expression for the speed is,

$v=\frac{c}{n}$  

Substitute all the values in the above equation,

$$\begin{gathered} v=\frac{2.998\times {10}^{8}m/s}{1.47} \\ =2.04\times {10}^{8}m/s \end{gathered}$$

Thus, the speed with which light reaches the retina is  $2.04\times {10}^{8}m/s$

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

The refractive index n = 1.47 . So the shift in wavelength is,

 

$$\begin{gathered} \lambda =\frac{{\lambda }_0}{n} \\ =\frac{650 nm}{1.47} \\ =442 nm \end{gathered}$$

Thus, the wavelength in the liquid is 442 nm.