Critical Angle

When light goes from a denser medium to a less dense medium, at a certain angle of incidence, the refracted ray goes along the boundary between the two media. The incident angle on this occasion is call the critical angle for the substances.

μg = sin 90 / sin c

sin c = 1/ μg

c = sin^-11/ μg

c = sin^-1(1 / μ)

Total Internal Reflection

When light goes from a denser medium to a less dense medium, as the angle of incidence exceeds the critical angle, the ray reflects back to the denser medium. This phenomenon is called Total Internal Reflection.

Total Internal Reflection is a very efficient reflection, as the loss of light energy is almost negligible.

Uses and Effects of Total Internal Reflection

1) Reflecting prisms



In optical instruments, right-angled prisms are widely used to divert the course of light rays. As the total internal reflection takes place within them, the loss of light energy can be kept to a minimum. So, the prisms are preferred to mirrors for the purpose of reflection.


2) Mirage




On hot summer days or in the deserts, patches of water appear to us, some miles in front of us, only to find none when we approach them. This phenomenon is caused by the total internal reflection. The air layers on the ground become hot and less dense in these places and light, when comes down has to pass through these less-dense layers. At a certain point, the light exceeds the critical angles and the total internal reflection takes place on a vast scale, creating the illusive puddles of water.


3) Sparkles in diamonds




The sparkles inside diamonds are cause by total internal reflection. Diamond is well-known for its toughness - very dense and μ is very high; larger refractive index means smaller critical angle. Therefore, when light enters a diamond, the possibility of it being subjected to total internal reflection is very high, that in turn causes sparkles.


4) Optic fibres




Optic fibres revolutionized the communication that we take for granted today. This humble device - a thin flexible glass fibre with a coating - carries light through a distance of miles and miles, with a very little loss of its energy, thanks to total internal reflection. The trick is done by keeping the outer layer known as cladding less dense relative to the inner dense core - the first condition for total internal reflection. Since light enters almost parallel to the fibre, the angle of incidence is high and it easily exceeds the critical angle that triggers off the total internal reflection. The flexibility of the fibres, light weight, low cost and the ability to send light signals through them with very little loss of light, make then indispensable in modern communication networks.


5) Medical uses - the endoscope




This is an instrument consisting of optic fibres. It is used by the medical professionals to see inside the body. The flexibility of optic fibres contributed to the invention of this device.

Please answer the following questions.

1) ABC is a right-angled prism with AC being the longest side. A light ray enters through AC at right angles and hits AB, reflects and then goes out through BC. Show this prism can never be an isosceles prism.
2) A diver sees a circular patch on the surface of water. Calculate its radius, assuming the refractive index of water as 4/3.
3) An isosceles right-angled glass prism can be used for the total internal reflection, but not a similar ice one. Explain. Take μg = 1.5 and μw = 1.3
4) Optic fibres are used as bundles of thin fibres instead of a thick single one. Explain this.
5) A light ray has to be diverted by 180⁰ inside a right-angled prism. Show how this is achievable using a ray diagram.
6) Using a ray diagram show how two prisms are used to divert a ray of light inside a pair of binoculars while keeping the image the same way up.