Question

A light wave has a frequency of $4\times 10^{14}Hz$ and a wavelength of $5\times 10^{-7}m$ in a medium. The refractive index of the medium is

• A. 1.5
• B. 1.33
• C. 1.0
• D. 0.66

Answer 1

Answer: (A)

Frequency of light wave, $v=4\times 10^{14}Hz$
Wavelength, ${\lambda }_m=5\times 10^{-7}m$
Wavelength of light wave in air
${\lambda }_{\text{air }}=\frac{\text{ Velocity of light in air }}{\text{ Frequency of light }}$
$=\frac{3\times 10^8}{4\times 10^{14}}$
$=7.5\times 10^{-7}m$
$\therefore$ Refractive index of medium is given as
$\mu =\frac{{\lambda }_{\text{air }}}{{\lambda }_{\text{medium }}}=\frac{7.5\times 10^{-7}}{5\times 10^{-7}}$
$=1.5$