# Total Internal Reflection

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Total internal reflection refers to the complete reflection of a ray of light within an optically-denser medium from the surrounding surfaces of optically less dense media back into the denser medium.

• Light ray travel from an optically denser medium to a less dense medium.
• The angle of incidence must be greater than a certain angle, called the critical angle.

For a ray of light passing from an optically denser to a less dense medium, critical angle, c, is the angle of incidence at which the angle of refraction is $90^{\circ}$.

• When the angle of incidence is less than the critical angle, the ray passes out into the less dense medium.
• When the angle of incidence is greater than the critical angle, the ray is reflected back into the denser medium.

The equation relating critical angle, c and the refractive index, n is:

$\sin{\text{c}} = \frac{1}{n}$

Question: Why does the angle of refraction become $90^{\circ}$ and not more at the critical angle?

Answer: This is the limit the light ray an be refracted in air because the angle in air cannot be larger than $90^{\circ}$. When the angle of incidence is greater than the critical angle, all the light undergoes reflection.

Application of total internal reflection: Optical Fibres

Optical fibres are very fine, optically pure glass fibre through which light undergoes total internal reflection to transmit data from one end to the other.

• Optical fibres usually have polished surfaces coated with a material of suitable refractive index so that there is no loss of light through the sides of the fibre.
• They are used in bundles to transmit light to or receive light from inaccessible places, by repeated totally internal reflections within the fibre.
• Optical fibres are increasingly being used to replace metal telecommunication cables, the messages being encoded as digital pulses of light rather than as fluctuating electric current. They can carry more data and are more reliable.
• Bundles of optical fibres are also used in endoscopes to inspect otherwise inaccessible parts of machines or of the living body.