Question

The velocity of light in glass whose refractive index w.r.t air is $1.5$ is $2\times {10}^{8}m/s$. In a certain liquid, the velocity of light is found to be $2.5\times {10}^{8}m/s$. The refractive index of the liquid w.r.t air is

• A. $0.8$
• B. $0.9$
• C. $1.2$
• D. $1.33$

Answer 1

The correct option is (C) $1.2$

Velocity of light in glass $\left(v_1\right)=2\times {10}^{8}m/s$

Refractive index of glass w.r.t air $\left({\eta }_1\right)=1.5$

Velocity of light in certain liquid $v_2=2\times {10}^8$ m/s

Let refractive index of certain liquid w.r.t air $={\eta }_g$

We know,

$Refractiveindex=\frac{Velocityoflight}{Velocityoflightinmed}$

Or,

$\frac{{\eta }_1}{{\eta }_2}=\frac{V_2}{V_1}$

Or,

${\eta }_2=\frac{{\eta }_1{V}_1}{V_2}$

Putting all the values

${\eta }_2=\frac{31.5\times 2\times {10}^8}{52.5\times {10}^8}$

After solving

${\eta }_2=\frac{6}{5}=1.2$

$\therefore$ Refractive index of certain liquid$=1.2$