We know that when a light ray is refracted from a denser medium to a thinner medium, the refracted ray moves away from the perpendicular. As a result, the angle of refraction is larger than the incidence.
The line AB in the figure is the plane of separation between water and air. Here, water is dense medium and air is light medium.
- P1O rays come from the dense medium of water and are incident at point O on the diffraction surface. A part of the light beam is reflected back through the water in the path OR1 and the other part is refracted back through the air in the path OQ1. Here the angle of refraction ∠Q1ON is larger than any angle ∠P1ON1. As the value of the angle of incidence increases, the value of the angle of refraction increases, and in each case, refraction and reflection occur.
- As the angle of incidence increases, it reaches a certain value when the value of the angle of refraction is exactly 90°. In this case, the refracted ray OQ2 approaches the interface of the two mediums. The angle of incidence at this position is called the critical angle; ∠P2ON1 = angle of criticality (θc). In this case, the angle of refraction, ∠NOQ2 = 90°. Even in this case, a part of the incident beam is reflected back through the water in the path OR2.
- If the value of the angle of incidence is greater than the critical angle, i.e. i > θc (as in the case of P3O incident rays), no part of the incident light is refracted in the second medium. This ray is completely reflected back through the first medium in path OR3. This phenomenon is called internal total reflection. In this condition, the interface of the medium behaves like a mirror.
Critical Angle
When a light ray is refracted from a denser medium to a thinner medium, the angle of incidence for which the angle of refraction is 90°, i.e., the refracted ray reaches the separation surface of the two mediums, is called the critical angle of the said medium. The value of the critical angle depends on the colour of the incident light and the nature of the medium. For example, the angle of refraction for red light is greater than the angle of refraction for violet light in certain two media. Again, the critical angle of water with respect to air is 49°, but the critical angle of glass with respect to air is 42°.
The angle of refraction of glass with respect to air is 42°, meaning that if the light rays from the glass are incident on the interface of glass and air at an angle of 42°, the refracted ray will go along the interface of the two mediums, i.e., the angle of refraction will be 90°.
Total Internal Reflection
If a ray of light passes from a denser medium to a thinner medium and is incident on the diffraction surface at an angle of incidence greater than the critical angle of the two mediums, then the ray is not refracted in the thinner medium and is completely reflected back in the thicker medium. This phenomenon is called internal total reflection.
Conditions for Total Internal Reflection
For internal total reflection the following two conditions need to be fulfilled.
- Rays of light must pass through a dense medium and fall on the separation between the dense and the thin medium.
- The value of angle of incidence must be greater than the critical angle of the medium.
In which case Total Internal Reflection is Impossible
Total internal reflection does not occur when light rays pass from a thinner medium to a thicker medium. This is because the angle of refraction is smaller than the angle of incidence when refracted from a thinner medium to a denser medium. The angle of incidence may increase to a maximum of 90°, but still the value of the angle of refraction will be less than 90°, i.e., the ray will be refracted. Since the angle of incidence cannot be increased further, total internal reflection does not occur when light rays are refracted from a thinner medium to a thicker medium.
The reason for using the word 'Total'
During simple reflection, a part of the light incident on the separation between two media is reflected, and the rest is refracted by the second medium. But in internal reflection, no part of the light is refracted; all of the incident light is reflected from the separating surfaces of the two media and returned to the first medium. Hence this reflection is called total reflection. Reflections caused by internal total reflection are very bright because all the light is reflected back through the dense medium.
Relation between Critical Angle and Refractive Index of dense medium
Let ∠P2ON1 = θc = critical angle of water and air medium. In this case the refracted ray OQ2 approaches the plane of divergence of the medium i.e. the angle of refraction is 90°. If the refractive index of air relative to water is wμa,
Thus, the value of the critical angle depends on the index of refraction of one medium relative to the other. If the two mediums are a and b and μa > μb, then
A natural example of Total Internal Reflection
Mirage
A mirage is a type of visual illusion. This is a natural example of total reflection of light. It is usually found in desert regions and in colder countries.
- Desert Mirage: During the day, intense solar radiation heats the desert sands and the adjacent air layer. As a result, the density of that air layer decreases. As one rises, the temperature of the air decreases and the density of the air increases. So, if the air in the desert is fairly constant, we can divide the atmosphere near the surface into a number of imaginary horizontal layers. These layers are visualised in such a way that the density of air mediating any layer is approximately the same in all parts of that layer. But if going from the lower layer to the upper layer, the density of air increases.
A ray of light from a distant point P on a tree is refracted as it passes from the denser medium of air to the layer of the next thinner medium, and as a rule the refracted ray moves away from the perpendicular. That is why the value of the angle of incidence of the ray increases during incidence at each level. As a result, the angle of incidence becomes larger than the angle of incidence. Then the ray is not refracted but totally reflected. At O level, that situation is shown. The reflected ray now goes upwards. Then the beam passes successively from the lighter layer to the denser layer. As a result, the ray is gradually deflected perpendicularly and finally reaches the eye of the passerby (at E). A passerby’s eye cannot follow the curve of that ray. So, he thinks the ray is coming from point P’. That is, P’ is the mirror image of P. Thus, an inverted reflection of the whole tree is formed. So, the passerby can see the tree directly and also see the reverse reflection.
The density and refraction of the air layers are always changing due to the continuous changes in temperature. As a result, the direction of the light rays passing through the air layers is constantly changing. So, the passerby feels that the reflection is vibrating. The passer-by considers this inverted and vibrating reflection to be that of a water body, as a similar phenomenon occurs when standing in front of a body of water. This desert mirage is called the inferior mirage. For a similar reason, pitch roads appear glistening—as if wet—from a distance in the hot summer sun. This is also a mirage.
- Mirage of the winter country: The land surface temperature is very low in winter-dominated countries. As a result, the air near the surface is very cold and has the highest density. As you go up, the temperature of the air layer increases and the density decreases. So light rays travelling upwards from a distant object P are refracted from a denser medium to a thinner medium. As a result, the refracted ray moves away from the normal. As a result, sometimes the angle of incidence becomes larger than the angle of criticality. Then the ray undergoes total internal reflection. The ray now descends and passes from the lighter medium to the denser medium as it descends. As a result, the beam gradually moves in the perpendicular direction. When the fully reflected ray reaches the viewer’s eye, the rope appears to be coming from a point above. As a result, the viewer sees an inverted reflection of the object P’ hanging in the sky. This phenomenon is called superior mirage.
Sparkling of Diamond
The refractive index of diamond is 2.42, and the angle of refraction of diamond with respect to air is 24.4°. Diamond faces are cut in such a way that they have many surfaces. The beam penetrates the diamond through almost all surfaces. After entering the diamond, the beam undergoes multiple total internal reflections at different planes, and only a few planes allow the beam to exit. In fact, light rays are repeatedly reflected on different surfaces and finally fall on one surface in such a way that the angle of incidence of the rays is less than any. As a result, the rays can go out into the air through that floor. So, since the rays enter through many planes and exit through a few planes together, those few planes appear very bright.
Generally, precious stones have a higher refractive index, so their angle of refraction is lower. So, cutting them properly makes them look bright for total internal reflection.