Question

The frequency of a light wave in a material is $2\times {10}^{14}\text{Hz}$ and wavelength is $5000\stackrel{\circ }{\text{A}}$. The refractive index of material will be

• A. $1.33$
• B. $1.40$
• C. $1.50$
• D. $3.0$

Answer 1

The correct option is D $3.0$

Let $v_m$ be the velocity of light in given medium.

From relation,
$\mu =\frac{c}{{\upsilon }_m}$
$\Rightarrow \mu =\frac{c}{{\nu }_m{\lambda }_m}$

$(\because \upsilon =\nu \lambda ,\lambda =5000{\text{A}}^{\circ })$

$\Rightarrow \mu =\frac{3\times {10}^8}{(2\times {10}^{14})(5000\times {10}^{-10})}$
$\Rightarrow \mu =\frac{3\times {10}^8}{{10}^4\times {10}^4}$
$\therefore \mu =3$

Hence, option $\left(d\right)$ is the correct answer.

Why this question? It tests your understanding of basic definition of the refractive index of a material and its relation with velocity of light in medium.