What is the critical angle when a ray of light passes through a glass prism? How does the angle of deviation depend upon the angle of incidence?

Answer 1

Hi there!

Not sure how familiar you are with Physics, but this question is referring to a law of physics known as Snell's Law. If we let θ₁= the angle the incident light makes with the prism and θ₂ = the angle the deviated light makes with the prism, then snell's law tells us that

sinθ₂ / sinθ₁ = n₁/n₂

(where n₁ and n₂ are the indices of refraction of our media, in this case n₁ is the index of refraction of air and n₂ is the index of refraction of glass)

So, if we solve the above equation for the angle of deviation, θ₂, we have

θ₂ = sin^-1(n₁/n₂ * sinθ₁)

Which gives us the relationship between angle of deviation and angle of incidence.

Now, we define the critical angle, θ_crit, as the largest possible angle of incidence for which incidence results in a refracted ray (rather than a reflected one). If you do the math, you end up finding that the critical angle is the value of θ₁ for which θ₂ = 90° (recall that sin90° = 1).

So, if we return to our first equation

sin90 / sinθ_crit = 1 / sinθ_crit = n₁/n₂

or, solving for θ_crit,

θ_crit = sin^-1(n₂ / n₁)

Hope that helps! Let me know if you have any further questions.