As shown in the figure, after passing through the medium 1 . The speed of light v₂ in medium 2 will be :
( Given c=3 × 10⁸ ms⁻¹ )

Solution

Physics sir · 4 steps

The speed in a medium depends only on that medium's own μᵣ and εᵣ, so look at medium 2.

1. Speed in a medium. Light travels at c in vacuum and slows down in a material by the factor √(μᵣ εᵣ), which is the refractive index n of that material.

   v = c/√(μᵣ εᵣ)

2. Medium 1 drops out. The speed inside a medium does not depend on where the light came from. Medium 1 sets the speed only while the light is inside it, so its value εᵣ = 4 does not enter v₂.
3. Put in numbers. For medium 2, μᵣ = 1 and εᵣ = 9, so √(1 × 9) = 3. Then v₂ = (3 × 10⁸)/3 = 1.0 × 10⁸ m s⁻¹.
4. So. The speed of light in medium 2 is 1.0 × 10⁸ m s⁻¹, option (a).

The idea to keep. Refractive index n = √(μᵣ εᵣ) and v = c/n. Each medium sets its own speed; the media the light crossed earlier do not matter.

Answer from the NTA final answer key. Solution by PrepWiser.