Physics– Light JEE MAINS simple sums

Question

The velocity of light in air is 3 * 10^8 ms-¹ and the velocity of light in a medium is 2 * 10^8 ms-¹. The critical angle for the pair is sin-¹ .? 

 

Answer 1

Starting with the general Snell's law

 

n₁ sin[θ₁] = n₂ sin[θ₂],

 

the critical angle (θ_c) occurs when θ_c = 90 deg. Since sin[90 deg] = 1, we have

 

θ_c = sin^-1[n₂ / n₁].

 

I will assume medium 2 is vacuum, so n₂ = 1; medium 1 is non-vacuum, so n₁ = (3 * 10⁸ m / s) / (2 * 10⁸ m / s) = 3 / 2. Plugging these in, we have

 

θ_c = sin^-1[n₂ / n₁] = sin^-1[2 / 3] = 41.8 deg.

 

Note that doing it the other way (medium 1 is vacuum) will not produce a solution, which means that you cannot have critical angle behavior when light goes from a medium with a lower index to one with a higher index.