Theory of Total Internal Reflection
The optical principles behind every demonstration in the lab.
Snell's Law
When light passes from one medium to another, it bends according to Snell's law. For light travelling from a denser medium (refractive index μ) to a rarer medium (air, μ = 1):
\[ \mu \sin i = \sin r \]Critical Angle
The critical angle C is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly 90°.
\[ \sin C = \frac{1}{\mu} \quad\Longleftrightarrow\quad \mu = \frac{1}{\sin C} \]Three Cases at the Interface
- i < C — light refracts into the rarer medium, bending away from the normal.
- i = C — the refracted ray grazes along the interface (r = 90°).
- i > C — Total Internal Reflection. 100% of light is reflected back.
Conditions for TIR
- Light must travel from a denser to a rarer medium.
- The angle of incidence must be greater than the critical angle.
Critical Angle Table (w.r.t. air)
| Substance | μ | C |
|---|---|---|
| Water | 1.33 | 48.75° |
| Turpentine | 1.47 | 42.86° |
| Glass | 1.50 | 41.81° |
| Flint Glass | 1.57 | 39.56° |
| Diamond | 2.41 | 24.52° |
Factors Affecting the Critical Angle
- Wavelength of light: μ decreases with wavelength, so C is smallest for violet and largest for red.
- Temperature: increasing temperature lowers μ, so C increases with temperature.
TIR in Prisms
- 45°-90°-45°: one TIR deviates light by 90°; two TIRs reverse it by 180°; can also erect an inverted image without lateral deviation.
- Equilateral (60°): light refracts at one face, may undergo TIR at another depending on geometry and μ.
- 30°-60°-90°: used for deviations less than 60° via TIR on the hypotenuse.