Principles of Ray Tracing (1)

In geometrical optics, light is treated as rays, typically drawn as lines that propagate in a straight line from one point to another. Ray tracing is a method of determining how a ray will react to a surface or mirror. Rays are understood to propagate always in a straight line, however when entering an angled surface, rebounding from an angled surface or propagating through a different medium, there are a few techniques that are needed to reliably determine the direction and path of a light ray. The following properties are the basis for ray tracing.

Refractive Index

The refractive index is a property intrinsic to a medium that describes how fast or slow light propagates in the medium. Light speed in a vacuum is 3*10^8 m/s. Light speed will only get slower in real mediums. The formula for refractive index is the speed of light c devided by the velocity of light in the medium.


The refractive index of air is approximately 1. The refractive index of glass for instance is about 1.5. This has implications on how light will propage when changing from one medium to another.




Snell’s Law

Snell’s law uses the angle of incidence (incoming ray), the angle of refraction (exiting ray) and the refractive indexes of each medium at a boundary to determine the path of propagation. Consider the example below:


Snell’s Law: η1*sin(θ1) = η2*sin(θ2)

The angle of incidence and the angle of refraction are both with respect to the normal of the surface!


Fermat’s Principle

Fermat’s Principle is also demonstrated in the above figure. Fermat’s Principle states that the angle of incidence of a ray will be equal to the angle of reflection, but exiting from the other side of the normal of the surface.


Using these principles alone, many optical instruments and technologies can be designed and built that manipulate the direction of light rays.

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