The critical angle is the angle of incidence beyond which light traveling from a denser medium to a less dense medium is no longer refracted but instead is entirely reflected back into the denser medium. This phenomenon occurs when light moves from a medium with a higher refractive index $n_1$ to a medium with a lower refractive index $n_2$.
At this angle, the refracted ray runs along the boundary between the two media. The critical angle can be calculated using Snell's law: $$n_1 \sin \theta_c = n_2 \sin 90 \degree$$
Since $\sin 90 \degree = 1$, the formula simplifies to: $$\sin \theta_c = \dfrac{n_2}{n_1}$$ and $$ \theta_c = \sin^{-1}(\dfrac{n_2}{n_1})$$
Total internal reflection occurs when the angle of incidence in the denser medium is greater than the critical angle. Under these conditions, the light does not pass into the less dense medium at all. Instead, it is completely reflected back into the denser medium.
Conditions for Total Internal Reflection:
Consider light traveling from water ($n_1 = 1.33$) to air ($n_2 = 1$). Calculate the critical angle.
Using the simulation below, vary the refractive indices and practise calculating the critical angles.
Optical fibres have their core as the central part of the fibre where the light is transmitted. It has a higher refractive index than the cladding, which is the outer optical material surrounding the core. Light is introduced into the core of the optical fibre at one end, typically by a light-emitting diode (LED) or laser. When light enters the fibre, it travels through the core. If the angle of incidence (the angle at which the light hits the boundary between the core and cladding) is less than the critical angle, some light will refract into the cladding. The angle of incidence is usually greater than the critical angle, so that the light will not pass into the cladding but will be entirely reflected back into the core. This reflection continues along the length of the fibre, with the light bouncing off the core-cladding boundary repeatedly.
Optical fibres can carry a much higher amount of data at high speeds compared to traditional copper cables due to their high bandwidth capacity and speed.
The use of total internal reflection minimizes signal loss, allowing data to be transmitted over long distances without significant degradation.
Unlike copper cables, optical fibres are immune to electromagnetic interference, ensuring a clearer and more reliable signal.
Optical fibres are used in endoscopes to transmit light and images from inside the body to external viewing equipment, aiding in diagnosis and surgery.
Optical fibres can also deliver laser energy precisely to target tissues, used in various surgical procedures. This enables minimally invasive surgeries and diagnostic procedures, reducing patient recovery time and risk of complications.