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Q.
The frequency of a light wave in a material is $2 \times 10^{14} Hz$ and wavelength is $5000\,\mathring{A}$. The refractive index of material will be
JIPMERJIPMER 2009Ray Optics and Optical Instruments
Solution:
Velocity of light waves in material is
$v=v \lambda$ ...(i)
Refractive index of material is
$\mu=\frac{c}{v}$ ...(ii)
where $c$ is speed of light in vacuum or air
or $\mu=\frac{c}{v \lambda}$ ...(iii)
Given, $v=2 \times 10^{14} Hz$
$\lambda=5000 \mathring{A}=5000 \times 10^{-10} m$
$c=3 \times 10^{8} m / s$
Hence, from Eq. (iii), we get
$\mu=\frac{3 \times 10^{8}}{2 \times 10^{14} \times 5000 \times 10^{-10}}=3.00$