Refraction and total internal reflection, explained.
Light changes direction when it crosses between media with different refractive indices at oblique incidence. Entering a higher-index medium bends the ray toward the normal. Total internal reflection requires travel from higher to lower index above the critical angle.
The relationship to remember
Key formulas
- Snell’s law
- n₁ sin θ₁ = n₂ sin θ₂
- Angles measured from the normal
- Refracted angle
- θ₂ = arcsin(n₁ sin θ₁ / n₂)
- No solution means total internal reflection
- Critical angle
- θc = arcsin(n₂/n₁)
- Only when n₁ > n₂
- Refractive index
- n = c/v
- Speed of light in vacuum ÷ speed in the medium
- Law of reflection
- θᵣ = θ₁
- Reflected angle equals incident angle
Worked example
Problem. Light travels from water (n = 1.33) into air (n = 1.00). Find the refracted angle for a ray striking the surface at 30°, and the critical angle.
- sin θ₂ = n₁ sin θ₁ / n₂ = 1.33 × sin 30° / 1.00 = 0.665.
- θ₂ = arcsin(0.665) = 41.7°: the ray bends away from the normal as it leaves the water.
- Critical angle: θc = arcsin(1.00 / 1.33) = 48.8°.
- Rays meeting the surface at more than 48.8° are totally internally reflected.
Answer. The ray leaves at 41.7° from the normal; the critical angle for water to air is about 48.8°.
A quick check
From air (n = 1) into glass (n = 1.5) at 30°, the refracted angle is about 19.47°. From glass to air, the critical angle is about 41.81°.
Inside the default experiment
- sin θ₂ = n₁ sin θ₁ / n₂ = 0.3824.
- θ₂ = arcsin(0.3824) = 22.48° from the normal.
- Total internal reflection is not possible in this direction.
When this model applies
Flat interface between transparent media. Angles are measured from the normal; ray intensity and partial reflection are not modeled.
Make a prediction. Then test it.
Travel from glass to air. Find the angle where the refracted ray disappears.
Try it: Refraction & total internal reflection simulation ↗Frequently asked questions
Wondering about the why? Start here.
When does total internal reflection occur?
When n₁ > n₂ and the incident angle exceeds arcsin(n₂/n₁). At the critical angle, the refracted ray travels along the boundary.
Does light always bend at a boundary?
At normal incidence, its direction stays the same. There is also no directional change if both media have the same refractive index.