CRITICAL ANGLE AND TOTAL INTERNAL REFLECTION
Critical angle and total internal reflection are considered to be one of the most important topics of ray-optics. When a ray of light falls or is incident on a medium exhibiting lower index of refraction, the ray gets bent away from the normal and as a result the exit angle exceeds the incident angle. This type of reflection is termed as internal reflection. In such a case, the exit angle will try to approach 90° for a particular critical incident angle θc. When the incident angle exceeds the critical angles, the total internal reflection takes place.
Consider a ray of light that travels from a denser medium to a rarer medium. The angle of incidence for which the angle of refraction becomes 90° is called the critical angle. This is used for constructing totally reflecting prisms.
Sin C / Sin 90o = 2m1 = m2 / m1
When the angle of incidence of a ray travelling from denser to rarer medium is greater than the critical angle, no refraction occurs. The incident ray is totally reflected back into the same medium. Here the laws of reflection hold good. Some light is also reflected before the critical angle is achieved, but not totally.
Usually, in most of the cases, the total reflection takes place at the periphery between transparent media when the index of refraction of the medium in which the ray of light lies is higher and it tries to move towards the other medium but at an angle of incidence which exceeds the critical angle. The value of the critical angle is 48.5° for a water-air surface. The indices of refraction depend on the wavelength, so as the wavelength changes, it brings about a change in the critical angle. Till the angles lesser than the critical angles, both reflection and refraction may take place but usually occur in varying amounts.
Applications of Total Internal Reflection:
Total Internal Reflection is applied in numerous fields like:
- This phenomenon helps in understanding the movement of light in optical fibers.
- Monolithic ring resonators can be fabricated where total internal reflection occurs at all or some of the interfaces.
- It is also used in slab lasers. It helps one to understand a zig-zag path through the medium.
The effect can also be disadvantageous:
As stated above, in case of slab lasers, total internal reflection might lead to parasitic lasing. It also makes it difficult to efficiently and easily extract the generated light in case of light-emitting diodes.
Illustration: A point source of light a placed at the bottom of a tank containing a liquid of refractive index μ. The level of the liquid is at a height h above the bottom of the tank. A bright circular spot is seen on the surface of the liquid when viewed from above. Find the radius of the spot?
Solution: The rays of light emerging from the source, which are incident at an angle q > qc. (Where is the critical angle) will be reflected.
Sin qc = m-