Question

If sum of velocities of light in two media is $3.25\times {10}^{8}m/s$ and their difference is $0.75\times {10}^{8}m/s$, find the refractive index of the second medium with respect to one :

• A. 1.25
• B. 1.6
• C. 1.5
• D. 1.3

Answer 1

Answer: (B)

1.6

Let the two velocities be $v_1$ and $v_2$.

$\therefore$ $v_1+v_2=3.25\times {10}^{8}m/s$ ......(1)

Also $v_2-v_1=0.75\times {10}^{8}m/s$

Thus we get $v_2=0.75\times {10}^8+v_1$

Putting it in (1), we get $0.75\times {10}^8+2v_1=3.25\times {10}^8$

$⟹$ $v_2=1.25\times {10}^{8}m/s$

Similarly, we get $v_1=2\times {10}^{8}m/s$

Refractive index of medium 2 w.r.t 1 $n_{21}=\frac{v_1}{v_2}$

$⟹$ $n_{21}=\frac{2}{1.25}=1.6$