Question

The velocity of light in glass ($\mu =1.5$) is $2\times {10}^{8}m/s$ and in certain liquid($\mu =1.2$), the velocity of light found to be $2.50\times {10}^{8}m/s$. Then the refractive index of the liquid with respect to glass is $0.8$

• A. True
• B. False

Answer 1

The correct option is A

True

We know that Refractive index of medium A $=\frac{V}{V_A}$

where, V is the speed in vacuum

and $V_A$ is the speed in medium A.

Refractive index of medium A w.r.t B is given by,

${\mu }_{\frac{A}{B}}=\frac{{\mu }_A}{{\mu }_B}=\frac{V_B}{V_A}$

Speed of light in glass, $V_g=2\times {10}^8\text{m}/\text{s}$

Speed of light in liquid $V_l=2.5\times {10}^8{\text{ms}}^{-1}$

So, Refractive index of liquid w.r.t glass

${\mu }_{\frac{l}{g}}=\frac{V_g}{V_l}=\frac{2\times {10}^8{\text{ms}}^{-1}}{2.5\times {10}^8{\text{ms}}^{-1}}=\frac{2}{2.5}=0.8$

So, the statement is true.