Air to water
\(n_1 = 1.00, n_2 = 1.33, \theta_1 = 30^{\circ} \rightarrow \theta_2 \approx 22.1^{\circ}\)
Snell's Law Calculator
Calculate refraction angles using Snell's law with interactive visualizations
Explore refraction at the interface
Drag the refractive indices and the incident angle. The refracted ray (green) appears in medium 2; if total internal reflection is triggered, the reflected ray (red) stays in medium 1.
Quick presets
1.00
1.003.00
1.50
1.003.00
30 °
089
Predict what will happen
When light goes from a denser medium to a less dense one, what happens past the critical angle?
Try the 'Diamond → Air' preset and increase θ₁.
Notice
Going from a less dense medium (lower n) into a denser one (higher n) bends the ray TOWARD the normal. The reverse bends it AWAY from the normal.
Common mistake
Both θ₁ and θ₂ are measured from the NORMAL (the dashed vertical line), not from the surface. A 30° incident angle means 30° off the normal, i.e. 60° off the interface.
Why it works
Light slows down in denser media (n = c / v). Snell's law expresses conservation of phase along the interface — the wavefront's component parallel to the interface is preserved.
Results
Final Answer
Refraction: \(\theta_2 = 19.47^{\circ}\)
Step-by-step Solution
- Snell's Law: \(n_1 \sin\theta_1 = n_2 \sin\theta_2\)
- Given: \(n_1 = 1.00\), \(n_2 = 1.50\), \(\theta_1 = 30^{\circ}\)
- Solve for θ₂: \(\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right) = 19.5^{\circ}\)
Theory & Formula
Snell's Law describes how light bends when passing between media with different refractive indices.
The refractive index n equals the ratio of the speed of light in vacuum to its speed in the medium. Higher n means slower light and a denser optical medium.
Total internal reflection Total internal reflection occurs when light goes from a denser to a less dense medium and the incident angle exceeds the critical angle \(\theta_c = \arcsin(n_2/n_1)\).
\(n_1 \sin\theta_1 = n_2 \sin\theta_2\)
Worked Examples
Glass to air
\(n_1 = 1.52, n_2 = 1.00, \theta_1 = 30^{\circ} \rightarrow \theta_2 \approx 49.5^{\circ}\)
External educational resource
Explore bending light in PhET
Open PhET's Bending Light simulation to drag light rays across boundaries between materials and watch refraction in real time.
PhET Interactive Simulations, University of Colorado Boulder