Question

A light of wavelength 6000 A in air, enters a medium with refractive index 1.5. What will be frequency and wavelength of light in the medium?

Answer 1

In air velocity of light is $3\times {10}^{8}m/s$ and wavelength is $6000A^o=6000\times {10}^{-10}m$

We know that $c=\lambda \times f$ , $f=frequency$

$3\times {10}^8=6000\times {10}^{-10}\times f$

$f=5\times {10}^{14}Hz$

We know that refractive index $n=\frac{velocityoflightinvacuum}{velocityoflightinmedium}=\frac{c}{v}$

Here $c=3\times {10}^{8}m/s$

So $1.5=\frac{3\times {10}^8}{v}$

$⟹v=2\times {10}^{8}m/s$

Since frequency does not change when light enters from one medium to other.

$v=\lambda f$

$2\times {10}^8=\lambda \times 5\times {10}^{14}$

$\lambda =4\times {10}^{-7}m=4000A^o$