Time taken by light to travel in two different materials A and B of refractive indices μ A and μ B of same thickness is t 1 and t 2 respectively. If t2-t1=5 × 10-10 s and the ratio of μ A to μ B is 1: 2. Then the thickness of material, in meter is: (Given vA and vB are velocities of light in A and B materials respectively).

Question

Time taken by light to travel in two different materials A and B of refractive indices μ A and μ B of same thickness is t 1 and t 2 respectively. If t2-t1=5 × 10-10 s and the ratio of μ A to μ B is 1: 2. Then the thickness of material, in meter is: (Given vA and vB are velocities of light in A and B materials respectively). (A) 5 × 10-10 v a m (B) 5 × 10-10 m (C) 1.5 × 10-10 m (D) 5 × 10-10 v B m

Tardigrade Admin · Accepted Answer

(μ A /μ B )=( c / V A / c / V B )=( V B / V A )=(1/2) Let the thickness is d ( d / v B )-( d / v A )=5 × 10-10 d =(5 × 10-10 × v A v B / v A - v B ) As v A =2 v B ⇒ d =5 × 10-10 × 2 v B Or d =5 × 10-10 × v A

$5 \times 1 0^{- 10} v_{a} m$

$5 \times 1 0^{- 10} m$

$1.5 \times 1 0^{- 10} m$

$5 \times 1 0^{- 10} v_{B} m$

5×10−10va​m

5×10−10m

1.5×10−10m

5×10−10vB​m

μB​μA​​=c/VB​c/VA​​=VA​VB​​=21​ Let the thickness is d vB​d​−vA​d​=5×10−10 d=vA​−vB​5×10−10×vA​vB​​ As vA​=2vB​⇒d=5×10−10×2vB​ Or d=5×10−10×vA​

$5 \times 1 0^{- 10} v_{a} m$

$5 \times 1 0^{- 10} m$

$1.5 \times 1 0^{- 10} m$

$5 \times 1 0^{- 10} v_{B} m$