Question

the ratio of thickness of two plates of two transparent medium A and B is 16:5.if time taken by light through A is twice than that of B then refractive index of A with respect to B will be​

Answer 1

Given that,

The ratio of thickness of two plates of two transparent medium A and B is 16:5.

To find,

The refractive index of A with respect to B.

Solution,

The refractive index of A with respect to B is given by the formula as follows :

$_B\mu ^A=\dfrac{\mu_ A}{\mu _B}$

Ratio of thickness, $\dfrac{d_A}{d_B}=\dfrac{16}{5}$ ....(1)

Since, time taken by light through A is twice than that of B. So,

$t_A=2t_B$

Time=distance/velocity

So,

$\dfrac{d_A}{v_A}=\dfrac{2d_B}{v_B}\\\\\dfrac{d_A}{d_B}=2\dfrac{v_A}{v_B}$

From equation (1)

$\dfrac{16}{5}=2\dfrac{v_A}{v_B}\\\\\dfrac{v_A}{v_B}=\dfrac{8}{5}$ .....(2)

It implies, $_B\mu ^A=\dfrac{\mu_ A}{\mu _B}=\dfrac{v_A}{v_B}$

From equation (2)

$\dfrac{\mu_ A}{\mu _B}=\dfrac{8}{5}\\\\=1.6$

So, the refractive index of A wrt B is 1.6