What is the critical angle for a light ray passing through glass and then into water?

Question

What is the critical angle for a light ray passing through glass and then into water?

Answer 1

The first thing we should do is draw a picture of the light ray traveling through the glass and then refracting at some angle once it reaches the water.

Now we can solve our problem.

Snell's Law tells us:

(1) n_glass x sinθ₁ = n_water x sinθ₂

The critical angle occurs when θ₂ (the angle of refraction) equals 90°.

So, sinθ₂ = 1, and we are left with:

(2) n_glass x sinθ₁ = n_water

(3) sinθ₁ = n_water / n_glass

Now we look up the indices of refraction for water and glass and solve for θ₁, our critical angle.

It is important to note that this only holds true when moving from a medium with a higher index of refraction to one with a lower index of refraction (n₁ > n₂). In this case, the light is moving from glass (higher n) to water (lower n), so we are ok.

I would also like to note that there is a "special" formula for finding the critical angle, which is

sinθ₁ = n₂ / n₁ (equation (3) in our solution)

However, as you can see, it is simply derived from Snell's Law, where the critical angle is found by understanding that the critical angle, θ₁, occurs when the angle of refraction, θ₂ = 90°. I am a big fan of memorizing less and understanding more.

Hope this helps!