How do Snell's Law and Total Internal Reflection work?
When a light beam crosses the boundary between two transparent materials with different refractive indices ($n = c/v$), its phase velocity changes and the ray bends at the interface. The mathematical relationship was discovered by Willebrord Snellius and René Descartes in the 17th century: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $\theta_1$ and $\theta_2$ are always measured relative to the normal line (perpendicular to the surface).
When light enters an optically denser medium such as water ($n_2 = 1.33$) or diamond ($n_2 = 2.42$) from air ($n_1 = 1.00$), the refracted ray bends toward the normal ($\theta_2 < \theta_1$). Conversely, when light travels from a higher-index medium into a lower-index medium ($n_1 > n_2$), the refracted ray bends away from the normal ($\theta_2 > \theta_1$).
As you increase $\theta_1$ when $n_1 > n_2$, the refracted angle eventually reaches $\theta_2 = 90^\circ$ (skimming along the interface). This threshold is the critical angle: $\theta_c = \arcsin(n_2 / n_1)$. For any incidence angle greater than $\theta_c$, zero light escapes into the second medium and Total Internal Reflection (TIR) occurs—the fundamental physics behind subsea fiber-optic telecommunications and medical endoscopes.
Step-by-step guided experiment
1. The brilliance of diamond: Select the Air → Diamond preset ($n_2 = 2.42$). At $\theta_1 = 45^\circ$, notice the refracted beam bends sharply to $\theta_2 = 17.0^\circ$ as light slows down to $123,881\text{ km/s}$.
2. Fiber optics in action: Select the Glass ($n_1 = 1.52$) → Air ($n_2 = 1.00$) preset. Notice the critical angle is $\theta_c = 41.1^\circ$. Sweep $\theta_1$ across $41^\circ$ to see the refracted beam vanish and $100\%$ of the laser energy reflect back inside the glass.
Frequently Asked Questions (FAQ)
What does Snell's Law of refraction state?
It states that the product of the first medium's refractive index and the sine of the angle of incidence equals the product of the second medium's index and the sine of the angle of refraction: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$.
When does Total Internal Reflection (the principle of fiber optics) occur?
It occurs only when light travels from an optically denser medium into a less dense medium ($n_1 > n_2$) and the incidence angle exceeds the critical angle $\theta_c = \arcsin(n_2 / n_1)$. At that point $100\%$ of the light reflects back without crossing the boundary.
How does the speed of light change inside water or diamond?
The phase velocity of light in a medium of refractive index $n$ is $v = c / n$, where $c \approx 300,000\text{ km/s}$. In water ($n = 1.333$) it slows to $\sim 225,000\text{ km/s}$, and in diamond ($n = 2.417$) it drops to $\sim 124,000\text{ km/s}$.
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