Subject overview
Total Internal Reflection
Calculate the critical angle from refractive indices, test an incidence angle and follow reflected and refracted rays across an optical interface.
01 Total Internal Reflection
Variables
- n1refractive index of incident medium
- 1dimensionless
- n2refractive index of second medium
- 1dimensionless
- θ1angle of incidence
- radradian
- θ2angle of refraction
- radradian
- θccritical angle
- radradian
Key Formulas
Requires trigonometry and inverse sine. As the incidence angle increases from a higher-index medium into a lower-index medium, the refracted ray bends farther from the normal. At the critical angle its limiting angle is π/2; substituting sin(π/2) = 1 into Snell’s law gives sin θc = n₂/n₁.
Above the critical angle there is no real propagating refraction angle. For n₁ ≤ n₂, total internal reflection cannot occur in this direction. At equal indices the interface does not bend or reflect the ray in this ideal model.
Light travels from medium 1 into medium 2. All angles are measured from the normal, not from the surface.
Flat interface between homogeneous, isotropic, non-magnetic, transparent media with positive real refractive indices at the same wavelength. Ray paths only: polarization, reflected/transmitted intensities and the evanescent field are not calculated.
Calculate
Type prefixes directly: 1.5k, 250m or 20u. Results: 3 significant figures.
Light travels from medium 1 into medium 2. All angles are measured from the normal, not from the surface.
Enter both refractive indices to find whether total internal reflection is possible.
Flat interface between homogeneous, isotropic, non-magnetic, transparent media with positive real refractive indices at the same wavelength. Ray paths only: polarization, reflected/transmitted intensities and the evanescent field are not calculated.