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

Step-by-step 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=(c)/(v)\\\\v=(c)/(n)\\\\v=(3* 10^8)/(1.56)\\\\v=1.92* 10^8\ m/s`

(b) The wavelength of light in material,

`\lambda=(\lambda_o)/(n)`

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

`\lambda_1=(\lambda_o)/(n)\\\\\lambda_1=(620* 10^(-9))/(1.56)\\\\\lambda_1=3.97* 10^(-7)\ m`

Hence, this is the required solution.