The difference in speed of light in the two media A and B (v_A − v_B) is 2.6 × 10⁷ m/s. If the refractive index of medium B is 1.47, then the ratio of the refractive index of medium B to medium A is : (Given: speed of light in vacuum c = 3 × 10⁸ ms⁻¹)

CONCEPT:

The velocity of the light in a medium is equal to the ratio of the speed of light in a vacuum to the refractive index and it is written as;

v = c/μ 

Here we have c as the speed of light in a vacuum, μ is the refractive index and v is the velocity of a given medium.

CALCULATION:

Given: vA − vB = 2.6 × 107 m/s       -----(1)

μ = 1.47

speed of light in vacuum c = 3 × 108 ms^-1

The speed of light in medium B is written as;

v_B = \(\frac{c}{μ_B}\)

⇒ vB = \(\frac{3 \times 10^8}{1.47}\)

⇒ v_B = 2.04 \(\times\) 10⁸ m/s

Now, on putting this value in equation (1) we have;

vA − 2.04 \(\times\) 108  = 2.6 × 107 

⇒ v_A = 2.6 × 107 + 2.04 \(\times\) 10⁸

⇒ v_A = 2.6 × 107 + 20.4 \(\times\) 10⁷

⇒ v_A = (2.6+20.4)  \(\times\) 10⁷

⇒ v_A = 23  \(\times\) 10⁷ m/s

Now, the speed of light in medium A is written as;

v_A = \(\frac{c}{μ_A}\)     -----(2)