When does refraction take place?

[MHD93]

When does refraction take place!?

For refraction of light rays to occur, rays should travel from one medium to another, but what exactly is the boundary between two media? For example, will light rays from (dirt stuck on a lens SURFACE or a finger touching the surface) undergo refraction from this surface or not? I'm asking because I doubt if there is (on a small scale) a layer of air gas (or say vacuum) in between working as a second medium, or not? (I just can't see what exactly the boundary is.)

 

[Ibix]

Refraction occurs at the boundary between any two materials with different refractive indices. If you have a layer of oil, or an anti-reflection coating, or are simply looking through the glass of a fish tank, you get refraction at each interface. For example, in the fish tank light rays refract at the air-glass boundary and again at the glass-water boundary.

Your example of dirt or a fingerprint is a bit different. Neither of those things is a smooth surface, so you're most likely to get scattering off them rather than any nice smooth refraction.

Basically draw a cross-section through your optical elements. Anywhere you have to draw a line, you've got a boundary. If the boundary is nice a smooth you get refraction; if the boundary is a mess you get scattering.

I'm not sure if you were asking about this, but if you zoom right in on a smooth surface you'll see it's made up of atoms and is not really smooth at all. It gets very difficult to define the surface in any sensible way. At that level, then, you can't really talk about light rays and surfaces; you need to consider the details of the interaction between the electromagnetic wave and the individual atoms.

Does that help?

 

[UltrafastPED]

For many purposes refraction occurs at an interface between two media with distinct indices of refraction.

But every transparent medium has an index of refraction, and it is possible for this index to vary continuously with temperature or pressure, or some other parameter such as mixing ratios of gasses, or concentrations of chemicals in solution ... the lens of the human eye is another example with a variation of index of refraction with distance from the edge; see GRIN lenses: http://en.wikipedia.org/wiki/Gradient-index_optics

In the case of continuously varying index of refraction there is a slight refraction with every distance; this is best described by Fermat's Principle ... or with the eikonal equation.

Here is a derivation of the eikonal equation, and an application to understanding how a mirage occurs:
http://people.seas.harvard.edu/~jones/ap216/lectures/ls_1/ls1_u2/ls1_unit_2.html