How and why does the internal reflaction occur?

Total internal reflection is an optical phenomenon that occurs when a ray of light strikes a medium boundary at an angle larger than the critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary no light can pass through, so effectively all of the light is reflected. The critical angle is the angle of incidence above which the total internal reflection occurs.

The critical angle is defined as the angle of incidence which provides an angle of refraction of 90-degrees.

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