Question

A light of wavelength $6000\mathring{A}$ in air centre a medium of refractive index $1.5$. What will be the frequency and wavelength of length in the medium?

Answer 1

Wavelength of light in air ${\lambda }_{air}=6000AV=6000\times {10}^{-18}cm/AV=6\times {10}^{-5}cm$

Velocity of light in air ${\nu }_{air}=3\times {10}^{10}cm/s$

Frequency of light in air $\nu =\frac{{\nu }_{air}}{{\lambda }_{air}}=\frac{3\times {10}^{10}}{6\times {10}^{-5}}=5\times {10}^{14}Hz$

On entering the medium of refractive index $\nu =1.5$ from air,

Velocity decreases to ${\nu }^{\prime }=\frac{\nu }{\mu }=\frac{3\times {10}^{10}}{1.5}=2\times {10}^{10}cm/s$

To keep the frequency unchanged, the wavelength of light in the medium also decreases by the same factor as the decrease in the velocity of light.

So altered wavelength of light in the medium ${\lambda }^{\prime }=\frac{6000AV}{1.5}=4000AV$

So frequency of light in the medium $=5\times {10}^{14}Hz$

Wavelength of light in the medium $=4000AV$