Snell's Law & Total Internal Reflection Cheat Sheet

Key Facts

• Snell's Law is $n_1 \sin \theta_1 = n_2 \sin \theta_2$, where angles are measured from the normal.
• The refractive index is $n = \frac{c}{v}$, where $c$ is the speed of light in vacuum and $v$ is the speed of light in the material.
• When light enters a higher-index material, $n_2 > n_1$, it slows down and bends toward the normal, so $\theta_2 < \theta_1$.
• When light enters a lower-index material, $n_2 < n_1$, it speeds up and bends away from the normal, so $\theta_2 > \theta_1$.
• The critical angle is found from $\sin \theta_c = \frac{n_2}{n_1}$ when light travels from a higher-index material to a lower-index material.
• Total internal reflection occurs only when $n_1 > n_2$ and the incident angle is greater than the critical angle, $\theta_1 > \theta_c$.
• At the critical angle, the refracted ray travels along the boundary, so $\theta_2 = 90^{\circ}$.
• Frequency stays the same during refraction, but speed and wavelength change according to $v = f\lambda$.

Vocabulary

Refraction

Refraction is the bending of light as it changes speed when moving from one medium into another.

Refractive Index

Refractive index $n$ measures how much a material slows light compared with its speed in vacuum.

Normal

The normal is an imaginary line drawn perpendicular to the surface where the light ray hits.

Incident Angle

The incident angle $\theta_1$ is the angle between the incoming ray and the normal.

Critical Angle

The critical angle $\theta_c$ is the incident angle that makes the refracted ray travel along the boundary at $90^{\circ}$.

Total Internal Reflection

Total internal reflection is the complete reflection of light inside a higher-index medium when the incident angle exceeds the critical angle.