CalculateY
Quick Answer
Light entering glass (n = 1.52) from air at 30 degrees refracts to approximately 19.2 degrees. At angles above approximately 41.1 degrees inside glass, light undergoes total internal reflection and does not pass into air.
Common Examples
| Input | Result |
|---|---|
| Air (n₁ = 1.0003), θ₁ = 30°, Glass (n₂ = 1.52) | θ₂ ≈ 19.20° |
| Air (n₁ = 1.0003), θ₁ = 45°, Water (n₂ = 1.333) | θ₂ ≈ 32.12° |
| Water (n₁ = 1.333), θ₁ = 40°, Air (n₂ = 1.0003) | θ₂ ≈ 58.93° |
| Glass (n₁ = 1.52), θ₁ = 60°, Air (n₂ = 1.0003) | Total internal reflection (critical angle ≈ 41.14°) |
| Diamond (n₁ = 2.417), θ₁ = 20°, Air (n₂ = 1.0003) | θ₂ ≈ 55.77° |
How It Works
Snell’s law
\[n_1 \sin(\theta_1) = n_2 \sin(\theta_2)\]Where:
- n₁ = refractive index of medium 1 (dimensionless, always >= 1)
- θ₁ = angle of incidence, measured from the normal to the surface
- n₂ = refractive index of medium 2
- θ₂ = angle of refraction, measured from the normal
A higher refractive index means light travels more slowly in that medium. When light enters a denser medium (higher n), it bends toward the normal, producing a smaller refraction angle. When it enters a less dense medium, it bends away from the normal.
Rearranged forms
- Angle of refraction: \(\theta_2 = \arcsin\left(\frac{n_1 \sin(\theta_1)}{n_2}\right)\)
- Angle of incidence: \(\theta_1 = \arcsin\left(\frac{n_2 \sin(\theta_2)}{n_1}\right)\)
- Refractive index: \(n_1 = \frac{n_2 \sin(\theta_2)}{\sin(\theta_1)}\)
Total internal reflection
When light travels from a denser medium to a less dense one (n₁ > n₂), there is a maximum angle of incidence beyond which no refraction occurs. All light is reflected back into the denser medium. This is called total internal reflection, and the threshold is the critical angle:
\[\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)\]For glass (n = 1.52) to air (n = 1.0003), the critical angle is approximately 41.1 degrees. Any incidence angle above this results in total internal reflection.
Common refractive indices
| Material | Refractive index |
|---|---|
| Vacuum | 1.0000 |
| Air | 1.0003 |
| Water | 1.333 |
| Glass (typical) | 1.52 |
| Diamond | 2.417 |
| Quartz | 1.544 |
| Sapphire | 1.77 |
Worked example
Light passes from air (n₁ = 1.0003) into glass (n₂ = 1.52) at an angle of 30 degrees from the normal.
\[1.0003 \times \sin(30°) = 1.52 \times \sin(\theta_2)\] \[\sin(\theta_2) = \frac{1.0003 \times 0.5}{1.52} = \frac{0.50015}{1.52} = 0.32905\] \[\theta_2 = \arcsin(0.32905) \approx 19.20°\]The light bends toward the normal as it enters the denser glass, reducing the angle from 30 degrees to approximately 19.2 degrees.