Question

A beam of light has a wavelength of 620 nm in vacuum.
a. What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.56? (Use 3.00×108 m/s for the speed of light in a vacuum.)
b. What is the wavelength of these waves in the liquid?

Answer 1

Explanation:

It is given that,

Wavelength of a beam of light in vacuum, $\lambda_o=620\ nm$

(a) Let v is the speed of light in a liquid whose index of refraction at this wavelength is 1.56.

We know that,

Refractive index,

$n=\dfrac{c}{v}\\\\v=\dfrac{c}{n}\\\\v=\dfrac{3\times 10^8}{1.56}\\\\v=1.92\times 10^8\ m/s$

(b) The wavelength of light in material,

$\lambda=\dfrac{\lambda_o}{n}$

Let $\lambda_1$ is the wavelength of these waves in the liquid. So,

$\lambda_1=\dfrac{\lambda_o}{n}\\\\\lambda_1=\dfrac{620\times 10^{-9}}{1.56}\\\\\lambda_1=3.97\times 10^{-7}\ m$

Hence, this is the required solution.