Total internal reflection

When does total internal reflection happen?

The critical angle is the angle at which the light waves stop being refracted, and are instead reflected.

If the angle of indicence is less than the critical angle, the light ray is refracted.
If the angle of indicence is more than the critical angle, the light ray is reflected.
If the angle of incidence is equal to the critical angle,

\sin\theta_c=\frac{n_2}{n_1}

We can figure this out from snell’s law! The angle of reflection/ refraction will always be 90\degree

To find just \theta_c (without the \sin):

\theta_c=\sin^{-1}(\frac{n_2}{n_1})

Question	Answer
What is total internal reflection?	Total internal reflection occurs when light travels from a medium with a higher refractive index (n_1) to a lower one (n_2) and the angle of incidence (i) is greater than the critical angle (\theta_c).
What are the two possible behaviors of light at a boundary?	The light wave can be refracted or reflected.
What is the critical angle?	The critical angle is the angle of incidence at which light stops being refracted and is instead reflected.
What happens if the angle of incidence is less than the critical angle?	The light ray is refracted.
What happens if the angle of incidence is greater than the critical angle?	The light ray is reflected.
What happens if the angle of incidence is equal to the critical angle?	The angle of refraction will always be 90\degree.
What is the formula for calculating the critical angle?	\sin\theta_c = \frac{n_2}{n_1}
How is the formula for critical angle derived from Snell’s Law?	From n_1\sin\theta_1 = n_2\sin\theta_2, substituting \theta_c and 90\degree gives n_1\sin\theta_c = n_2 \times 1, so n_1\sin\theta_c = n_2, which rearranges to \sin\theta_c = \frac{n_2}{n_1}.
How do you calculate the critical angle without sine?	\theta_c = \sin^{-1}(\frac{n_2}{n_1})