Time taken by light to travel in two different materials A and B of...

The speed of light in a medium is inversely proportional to the refractive index of the material. Therefore,

$\dfrac{{\mu}_{A}}{{\mu}_{B}} = \dfrac{{v}_{B}}{{v}_{A}} = \dfrac{1}{2}$

Let the thickness is $d$

$⇒ {t}_{2} - {t}_{1} = \dfrac{d}{{v}_{B}} - \dfrac{d}{{v}_{A}} = 5 \times {10}^{- 10}s$

As ${v}_{A} = 2{v}_{B} ⇒ d = 5 \times {10}^{- 10} \times 2{v}_{B}$

$⇒ d = 5 \times {10}^{- 10} \times {v}_{A}m$.