🔍 Geometric Optics & Wave Propagation
Snell's Law & Refraction Calculator
Compute angle of refraction ($\theta_2$), critical angle ($\theta_c$) for Total Internal Reflection (TIR), and light speed through optical media with refractive index presets.
💧 Air ➔ Water ($n=1.333$)
🪟 Air ➔ Crown Glass ($n=1.517$)
💎 Air ➔ Diamond ($n=2.417$)
🌊 Water ➔ Air (TIR Test)
💡 Fiber Optic Core/Clad
Optical Mediums & Angle
Air = 1.000
degrees (°)
Glass = 1.52
Angle of Refraction (θ₂)
27.78°
Critical Angle ($\theta_c$)
None ($n_1 < n_2$)
Light Speed in Med 2
197,627 km/s
0.659 c
Deviation Angle ($\delta$)
17.22°
💡 Snell's Identity:
$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \implies 1.000 \times \sin(45^\circ) = 1.517 \times \sin(27.8^\circ)$$
Principles of Optical Refraction
Willebrord Snellius formulated the law of refraction governing phase velocity changes:
$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \implies \theta_2 = \arcsin\left(\frac{n_1 \sin(\theta_1)}{n_2}\right)$$
- Speed of Light in Medium: $v = \frac{c}{n}$, where $c \approx 299,792,458\text{ m/s}$.
- Total Internal Reflection (TIR): Occurs only when passing from a denser to a rarer medium ($n_1 > n_2$) at angles $\theta_1 \ge \theta_c = \arcsin(n_2 / n_1)$.