Question

The velocity of light in glass whose refractive index with respect to air is $1.5$ is $2\times {10}^{8}m{s}^{-1}$and in certain liquid, the velocity of light is found to be $2.50\times {10}^{8}m{s}^{-1}$. Find the refractive index of that liquid with respect to air.

• A. 1
• B. 1.2
• C. 1.5
• D. 1.6

Answer 1

The correct option is B

1.2

Refractive index ($\mu$) is inversely proportional to velocity ($\nu$).
${\mathrm{Let\; \mu }}_l$ = Refractive index of liquid wrt air
${\mu }_g$=Refractive index of glass wrt air =1.5
${\nu }_l$= velocity of light in liquid =$2.5\times {10}^8$
${\nu }_g$ =velocity of light in glass =$2\times {10}^8$

$\mu \alpha \frac{1}{v}$
$\Rightarrow \frac{{\mu }_l}{{\mu }_g}=\frac{v_g}{v_l}$
$\Rightarrow \frac{{\mu }_l}{1.5}=\frac{2\times {10}^8}{2.5\times {10}^8}$
$\Rightarrow {\mu }_l=1.2$