Total Internal Reflection — Definition

Definition

Imagine you're looking at a fish in a pond. When light travels from the water (a denser medium) into the air (a rarer medium), it bends away from the normal. This bending is called refraction. Now, what if the light tries to leave the water at a very shallow angle? This is where Total Internal Reflection (TIR) comes into play.

TIR is a fascinating phenomenon where light, instead of passing from one medium to another, gets completely reflected back into the original medium. But this doesn't happen all the time; there are two crucial conditions for TIR to occur:

1
Light must travel from an optically denser medium to an optically rarer medium. — Think of water to air, glass to air, or even diamond to air. The 'denser' medium has a higher refractive index, meaning light travels slower in it. The 'rarer' medium has a lower refractive index, where light travels faster.
2
The angle of incidence in the denser medium must be greater than the critical angle. — The critical angle is a specific angle of incidence for a given pair of media, at which the refracted ray just grazes the interface, meaning it travels along the boundary between the two media. If the angle of incidence increases even slightly beyond this critical angle, the light can no longer refract into the rarer medium. Instead, it undergoes total internal reflection.

Let's visualize this: As light rays go from water to air, if the angle of incidence is small, they refract normally. As you increase the angle of incidence, the angle of refraction also increases, bending further away from the normal.

At a particular angle of incidence, the angle of refraction becomes $90^circ$. This special angle of incidence is called the critical angle ($i_c$ or $heta_c$). If the angle of incidence becomes even larger than the critical angle, the light cannot escape into the air; it hits the boundary and bounces back entirely into the water, just like it hit a mirror.

This is Total Internal Reflection.

This phenomenon is incredibly important and has many real-world applications, from the sparkling of diamonds to the transmission of data through optical fibers, and even the formation of mirages in deserts. Understanding TIR requires a good grasp of refraction and Snell's Law, as it's essentially an extreme case of refraction.