The speed of light decreases to half when it enters a medium from the air. Find the medium's refractive index with respect to air.

  
 $\mathrm{Refractive} \mathrm{index} \mathrm{of} \mathrm{a} \mathrm{medium}\left(\mathrm{\mu }\right)=\frac{\mathrm{velocity} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{vacuum}}{\mathrm{velocity} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{the} \mathrm{medium}}$

Let us say, the velocity of light in a vacuum is v₁ and the velocity of light in the medium is v₂

$\frac{{\mathrm{v}}_1}{2}={\mathrm{v}}_2$          ............ eq (i)

Hence, $\mu =\frac{v_1}{v_2}$     ............ eq (ii)

Put the value of $v_2$ from eq (i) into eq (ii) 

$$𝜇 = \frac{v_1}{v_1/2}$$

$$𝜇= 2$$

Hence, the refractive index of that medium with respect to air is 2.