Question

A monochromatic beam of light of wavelength $6000\stackrel{o}{\text{A}}$ in vacuum enters a medium of refractive index $1.25$. In the medium its wavelength and its frequency are

• A. $2400\stackrel{o}{\text{A}};5\times {10}^{14}\text{Hz}$
• B. $4800\stackrel{o}{\text{A}};5\times {10}^{14}\text{Hz}$
• C. $3200\stackrel{o}{\text{A}};5\times {10}^{12}\text{Hz}$
• D. $1800\stackrel{o}{\text{A}};5\times {10}^{13}\text{Hz}$

Answer 1

The correct option is B $4800\stackrel{o}{\text{A}};5\times {10}^{14}\text{Hz}$

$\mu =\frac{c_o}{c_m}=\frac{f{\lambda }_o}{f{\lambda }_m}$

When light travels from one medium to another, frequency of light remains constant, speed and wavelength will change.

${\lambda }_m=\frac{{\lambda }_o}{\mu }=\frac{6000\times {10}^{-10}}{1.25}=4800\times {10}^{-10}\text{m}=4800\stackrel{o}{\text{A}}$

$f=\frac{c_o}{{\lambda }_o}=\frac{3\times {10}^8}{6000\times {10}^{-10}}=5\times {10}^{14}\text{Hz}$