Question

Fill in the Blanks
A monochromatic beam of light of wavelength $6000\mathring{A}$ in vacuum enters a medium of refractive index $\mathrm{1.5.}$ In the medium its wavelength is _______ and frequency is________.

Answer 1

Refractive Index of medium$\left(\mu \right)=\frac{speedoflightinvaccum}{speedoflightinmedium}$

Also, Speed$=Wavelength\times Frequency$.

$\mu =\frac{c}{v}$ Also, frequency is same.

$\mu =\frac{\eta d_0}{\eta d_1}=\frac{d_0}{d_1}$

$\Rightarrow d_1=\frac{d_0}{\mu }$

$d_1=\frac{6000}{1.5}=4000A^{\circ }$

Frequency$\left(\eta \right)=\frac{c}{d_0}=\frac{3\times {10}^8}{6000\times {10}^{-10}}$

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

Frequency remains constant throughout

Wavelength is $4000A^{\circ }$ & frequency $=5\times {10}^{14}Hz$.