Refraction & Snell's Law Explorer

Adjust the incident angle and choose materials to see how light bends at the boundary between two media. Drag the ray on the diagram to explore refraction and total internal reflection. All calculations run in your browser.

Materials

Medium 1 (incident)

Medium 2 (transmitted)

Ray Diagram

Drag the red point to change the incident angle.

Incident rayReflected rayRefracted ray

Incident Angle

deg

Presets

Refracted Angle (θ₂)

22.04°

Critical Angle (θc)

N/A

Speed Ratio (v₁/v₂)

1.33

Step-by-Step Solution

n_1 \sin\theta_1 = n_2 \sin\theta_2

(1.0003)\sin(30^\circ) = (1.333)\sin\theta_2

(1.0003)(0.5) = (1.333)\sin\theta_2

\sin\theta_2 = \frac{1.0003 \times 0.5}{1.333} = 0.3752

\theta_2 = \arcsin(0.3752) = 22.04^\circ

Reference Guide

Snell's Law

When light crosses the boundary between two materials, it changes direction. Snell's law describes the relationship between the angles and the refractive indices of the two media.

n_1 \sin\theta_1 = n_2 \sin\theta_2

Variables

$n_1$ and $n_2$ are the refractive indices of the two media
$\theta_1$ is the angle of incidence (from the normal)
$\theta_2$ is the angle of refraction (from the normal)

Light bends toward the normal when entering a denser medium ( $n_2 > n_1$ ) and away from the normal when entering a less dense medium ( $n_2 < n_1$ ).

Total Internal Reflection

When light travels from a denser medium to a less dense one ( $n_1 > n_2$ ), there is a maximum angle of incidence beyond which no light passes through. All light is reflected back. This is total internal reflection (TIR).

\theta_c = \arcsin\!\left(\frac{n_2}{n_1}\right)

Applications

Fiber optics use TIR to carry light signals through glass cables with almost no loss
Diamonds sparkle because their high refractive index (2.42) gives a very small critical angle, trapping light inside
Prisms in binoculars use TIR to redirect light without mirrors

Refraction in Everyday Life

Refraction explains many everyday observations.

Pools look shallower than they are because light bending at the water surface shifts the apparent position of the bottom upward.
A straw in water looks bent at the surface because the light from the submerged part refracts when it exits the water.
Mirages on hot roads occur because air near the pavement has a lower refractive index, gradually bending light upward so you see sky reflected on the road.
Rainbows form when sunlight refracts entering a raindrop, reflects off the back, and refracts again exiting. Different wavelengths bend by different amounts, splitting white light into colors.

Speed of Light in Media

The refractive index of a material tells you how much light slows down compared to its speed in vacuum.

n = \frac{c}{v}

What this means

$c$ is the speed of light in vacuum ( $3 \times 10^8$ m/s)
$v$ is the speed of light in the medium
Higher $n$ means slower light. In water ( $n = 1.333$ ), light travels at about 75% of its vacuum speed
In diamond ( $n = 2.42$ ), light slows to about 41% of its vacuum speed

The change in speed is what causes light to bend. The wavefront enters the new medium at an angle, and one side slows down before the other, pivoting the direction of travel.