Total internal reflection (TIR) is an intriguing optical phenomenon where light is completely reflected back into its original medium upon striking a boundary at a specific angle.

TIR occurs when a propagating wave interacts with a boundary between two media at an angle greater than a critical angle relative to the normal of the surface. This phenomenon is observed when the refractive index of the second medium is lower than that of the first. If the incident angle exceeds this critical angle, the wave cannot penetrate the boundary and is entirely reflected back. This principle is widely applied in technologies such as optical fibers and prisms.

The critical angle is defined as the angle of incidence beyond which total internal reflection takes place. This angle is contingent upon the refractive indices of the two interacting media. It can be calculated using Snell’s law by setting the refraction angle to $90^\circ$. The critical angle can be expressed mathematically as:

where $n_1$ is the refractive index of the medium from which the light is originating, and $n_2$ is the refractive index of the medium into which the light is attempting to enter.

When light transitions from a medium with a higher refractive index to one with a lower refractive index, it accelerates. If the light strikes the boundary at an angle less than the critical angle, it refracts and continues into the second medium. Conversely, if the light impacts the boundary at an angle greater than the critical angle, it cannot enter the second medium and is instead completely reflected back into the first medium.

This phenomenon is harnessed in numerous practical applications. For example, in fiber optic cables, light signals are transmitted through thin strands of glass or plastic. Total internal reflection ensures that the light remains confined within the fiber, allowing it to travel vast distances without loss. Likewise, in devices such as binoculars and periscopes, prisms utilize total internal reflection to redirect light, allowing users to see around obstacles or over extended distances.

In conclusion, total internal reflection is a captivating and practical phenomenon that occurs when light traveling from a denser medium to a less dense medium encounters a boundary at an angle greater than the critical angle.