Question

Time taken by light to travel in two different materials A and B of refractive indices μA and μB of same thickness is t1 and t2 respectively. If t2 – t1 = 5 × 10–10 s and the ratio of μA to μB 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 vA m
• B. 5 × 10-10 m
• C. 1.5 × 10-10 m
• D. 5 × 10-10 vB m

Answer 1

Answer: (A)

5 × 10-10 vA m

Answer 2

$\frac{\mu_A}{\mu_B}$=$\frac{\frac{c}{V_A}}{\frac{c}{V_B}}$=$\frac{V_B}{V_A}$=$\frac{1}{2}$
Let the thickness be d
$\frac{d}{v_B}$−$\frac{d}{v_A}$=5×10−10
d=5×10−10×$\frac{v_Av_B}{v_A-v_B}$
As vA=2vB
⇒d=5×10−10×2vB
Or
d=5×10−10×vA