Question

A monochromatic beam of light of wavelength $6000\mathring{A}$ in a vacuum enter a medium of refractive index $1.5$. In the medium, find its wavelength (in $\mathring{A}$ )

Answer 1

Using the formula,

$c=\nu \lambda$, we have

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

$\lambda =6000\mathring{A}$

Thus, the frequency of the monochromatic beam of light is

$\nu =\frac{c}{\lambda }=\frac{3\times {10}^8}{6000\times {10}^{-10}}=0.5\times {10}^{15}Hz$

We know,

$\mu =\frac{c}{v}=\frac{Speedoflightinvacuum}{Speedoflightinmedium}$

Given,

$\mu =1.5$

$\Rightarrow v=\frac{c}{\mu }=\frac{3\times {10}^8}{1.5}=2\times {10}^{8}m/sec$

Wavelength of monochromatic beam in medium is given as

$\lambda =\frac{v}{\nu }=\frac{2\times {10}^8}{0.5\times {10}^{15}}=4\times {10}^{-7}m=4\times {10}^3\mathring{A}=4000\mathring{A}$

Hence, the wavelength of monochromatic beam of light in the medium is $4000\mathring{A}$.