Geometrical Optics

Refraction

A beam incident on a transparent medium (glass or water) is split into a reflected and a transmitted (refracted) beam. (Remember the bulldozer.)

Look at the aquarium!

Law of Refraction (Snell's Law)

  • Light going from a fast medium to slow medium bends towards the normal.

  • Light going from slow medium to fast bends away from normal.

The law of refraction is given by (view the demo.)


Try it! Refraction






Index of Refraction

n = c/v


Angle of transmission, for various angles of incidence, and various media


From To incident angle = 15 30 45 60 75 89
Air Water 11 22 32 41 47 49
Air Glass 10 19 28 35 40 42
Air Diamond 6 12 16 20 23 24
Glass Water 17 34 53 78 - -
GlassAir 23 49 - - - -


Total internal reflection

In the above table some entries are blank. The reason is that a beam that is trying to enter a faster medium (smaller n) at a larger angle of incident would have to be bent away from the normal more than 90o. This is not possible. Therefore nothing is transmitted, and everything is reflected. This is called total internal reflection. It only occurs at sufficiently large incident angles at the inside (internally) of a dense medium (larger n) bordered by a less dense medium (smaller n). Of course the law of reflection holds. The angle of incidence where total internal reflection first happens is called the critical angle.


Try it! Critical Angle of Reflection


Fiber Optics

An application of total internal reflection is fiber optics, the use of thin flexible glass or plastic fibers as light pipes. Light is sent down the fiber, which has a larger index of refraction than its surroundings. If the light in the fiber hits the surface at an angle of incidence greater than the critical angle, it is totally internally reflected, and there are no losses due to light escaping.

If the fiber is used to transmit a light signal consisting of a rapid series of pulses, it is important not only that all the light from a given pulse reach the other end of the fiber, but that it all arrive there at one time. Otherwise the pulse becomes spread out and might blur with the next pulse. Graded fibers with varying index of refraction can be made so that the time for rayis going straight down the center is the same as for rays bouncing from side to side. Such fibers are replacing metal wire for telephone lines andn for data transmission. In general, the higher the frequency of a wave used for communication, the more information can be transmitted per second. Since the frequency of visible light is much higher than radio frequencies, these fibers can carry many signals (or conversations) at the same time. Further, they do not radiate signals, so they cannot be bugged without directly connecting to them.

Dispersion

Index of Refraction:
  • c : speed of light in vacuum
  • v : speed of light in material

Snell's law rephrased
  • Light going from small n to large n is bent toward the normal.
  • Light going from large n to small n is bent away from the normal.


Index of Refraction in Various Media:

Mediumn n
Vacuum 1
Air 1.0003
Water 1.33
Glass 1.5
Diamond 2.4


Mirages and atmospheric distortions

A mirage is produced by the bending of light rays in the atmosphere when there are large temperature differences between the gound and the air.

A dark asphalt road will get very hot in the summer sun. When this happens, the air next to it may become much hotter than the higher air. This, in turn, can cause light to be bent so much that it appears reflected -- a mirage. In a rough way one can think of the effect as a gradual total internal reflection at the boundary between hot and cool air. When you look at the road ahead, you see a reflection in it of whatever lies ahead. The reflections of the sky are mostly associated with the appearance of water on the road.

We can see the sun after it has set below the geometrical horizon. The atmosphere is denser toward the bottom, less dense toward the top. The gradual change in density produces a gradual change in the index of refraction, which bends the light coming from the sun ( figure ). Here is an example of a sunset (Nova Scotia, Canada) .

Ch. Elster
Aug 26 14:27:03 EDT 2020