1. What happens when light moves from denser to rarer
When light goes from a denser medium (like glass or water) to a rarer medium (like air), it speeds up. Because of this, the refracted ray bends away from the normal.
If the incident angle keeps increasing, the bending becomes so large that at one special angle, the refracted ray just grazes along the boundary. That special angle is called the critical angle.
2. Critical angle: the key idea
The critical angle is the angle of incidence in the denser medium for which the angle of refraction becomes 90° in the rarer medium.
At this angle, the refracted ray does not enter the second medium — it travels right along the boundary.
2.1. Definition using Snell’s law
If \(i_c\) is the critical angle, then using Snell’s law:
\( n_1 \sin i_c = n_2 \sin 90^\circ \)
Since \( \sin 90^\circ = 1 \), this becomes:
\( \sin i_c = \dfrac{n_2}{n_1} \)
This is valid only when \( n_1 > n_2 \), meaning light is moving from a denser to a rarer medium.
3. When total internal reflection happens
Once the incident angle becomes greater than the critical angle, something interesting happens: all the light is reflected back into the denser medium. No refraction occurs.
This phenomenon is called Total Internal Reflection (TIR).
3.1. Conditions required for TIR
TIR happens only when both conditions below are satisfied:
- Light must travel from a denser medium to a rarer medium.
- The angle of incidence must be greater than the critical angle.
If either condition fails, TIR will not occur.
4. Why TIR occurs — physical idea
When the incident angle becomes very large, the wave inside the denser medium cannot bend enough to enter the rarer medium. Instead, the boundary behaves like a perfect mirror. The entire light wave bounces back.
I imagine it like trying to push a ray through the boundary at too steep an angle — it simply cannot escape.
5. Examples where I can see TIR directly
TIR is not just a theory — it’s behind many familiar effects:
- Diamond sparkle: Diamonds have a very high refractive index, so their critical angle is small. Light gets trapped inside and reflects many times, creating sparkle.
- Mirage: Hot air near the ground has a lower refractive index. Light bends so much that it stays inside a layer and reflects, creating an illusion of water.
- Optical fibres: Light repeatedly reflects inside the glass fibre due to TIR, allowing signals to travel long distances.
- Shining water surface: At shallow viewing angles, the water acts like a mirror because of TIR at the water–air boundary.
6. Critical angle values for some materials
Different materials have different critical angles:
| Material | Approx. Critical Angle |
|---|---|
| Glass–air | ≈ 42° |
| Water–air | ≈ 49° |
| Diamond–air | ≈ 24° |
Smaller critical angle → easier to get TIR. This is why diamond sparkles so strongly compared to glass.
7. A quick example to make it clearer
If light goes from glass (n = 1.5) to air (n = 1.0):
\( \sin i_c = \dfrac{1.0}{1.5} = 0.666... \)
So,
\( i_c \approx 41.8^\circ \)
If the angle of incidence is, say, \(50^\circ\), which is greater than \(41.8^\circ\), the ray will undergo total internal reflection.