Refraction & total internal reflection simulation
Shine a ray from one transparent material into another and watch it bend or reflect completely. Snell’s law, n₁ sin θ₁ = n₂ sin θ₂, gives the refracted angle. When light travels into a lower-index material at more than the critical angle θc = arcsin(n₂/n₁), no light is transmitted: total internal reflection. From glass (n = 1.5) to air, θc ≈ 41.8°.
What if you changed…
Travel from glass to air. Find the angle where the refracted ray disappears.
See the calculation
- 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.
What this model assumes
Flat interface between transparent media. Angles are measured from the normal; ray intensity and partial reflection are not modeled.
Keep an eye on this
Always measure the ray angle from the normal to the boundary, not from the boundary itself.
Understand the physics ↗Formulas used in this simulation
- 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
Refraction & total internal reflection: common questions
Wondering about the why? Start here.
What is total internal reflection?
When light inside a higher-index medium strikes a boundary with a lower-index medium at more than the critical angle, all of it reflects back inside. Optical fibres use this to guide light.
How do you calculate the critical angle?
θc = arcsin(n₂/n₁), where n₁ is the index of the medium the light is in and n₂ is smaller. For glass (1.5) to air (1.0), θc = arcsin(0.667) ≈ 41.8°.
Why does light bend toward the normal when it enters glass?
Light travels more slowly in glass than in air. Snell’s law then requires a smaller angle from the normal in the higher-index material.
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.