When a light ray crosses the boundary between two transparent media, its speed and direction generally change. Refraction is described by Snell's law.
The Law
n_1 \sin\theta_1 = n_2 \sin\theta_2- $n_1$, $n_2$ — indices of refraction of the incident and transmitting media
- $\theta_1$, $\theta_2$ — angles of incidence and refraction, measured from the surface normal
Index of refraction:
n = \frac{c}{v}where $c$ is the speed of light in vacuum and $v$ is the speed in the medium. Larger $n$ means slower light and usually stronger bending toward the normal when entering from air.
Qualitative Behavior
- Entering a higher-$n$ medium: ray bends toward the normal ($\theta_2 < \theta_1$)
- Entering a lower-$n$ medium: ray bends away from the normal
- Along the normal ($\theta_1 = 0$): no change in direction
Critical Angle and TIR
When light travels from higher $n$ to lower $n$, $\theta_2$ can reach 90°. The corresponding incidence angle is the critical angle:
\theta_c = \arcsin\!\left(\frac{n_2}{n_1}\right) \quad (n_1 > n_2)For $\theta_1 > \theta_c$, total internal reflection occurs: no transmitted ray in the second medium (ideal case). Optical fibers rely on this effect.
Worked Example
Light in water ($n_1 = 1.33$) hits glass ($n_2 = 1.50$) at $\theta_1 = 30^\circ$.
$\sin\theta_2 = (1.33/1.50)\sin 30^\circ = 0.443 ⇒ \theta_2 ≈ 26.3^\circ$
The ray bends toward the normal, as expected ($n_2 > n_1$).