Monochromatic light of wavelength 589 nm is incident from air on a water surface. If µ for water is 1.33, find the wavelength, frequency and speed of the refracted light.

#### Solution

Wavelength of light in air, λ = 589 nm

Therefore,

Frequency of light in air is given by

`f=c/lambda=(3xx10^8)/(589xx10^-9)=5.09xx10^14 Hz`

Since, frequency of light does not depend on the medium. Thus, the frequency of the refracted light in water will be equal to the frequency of the incident or reflected light in air.

Hence, the frequency of refracted light = `5.09xx10^14 Hz`

Now

Speed of light in water, `v=c/mu=(3xx10^8)/(1.33)=2.26xx10^8 `m/s

Wavelength of light in water,`lambda=v/f=(2.26xx10^8)/(5.09xx10^14)=444.007xx10^-9 "m or " 444.007 "nm"`

Therefore the speed, frequency and wavelength of refracted light are 2.26 × 10^{8} m/s, 5.09×10^{14} Hz and 444.007 nm, respectively.