Total internal reflection (T.I.R.)

[skywalker09]

Why is it that T.I.R. only occurs when a light is traveling from a denser to a rarer medium? Intuition suggests that this should happen when going from a rarer to a denser medium. Care to get into some mathematics?

Also, can the interface between 2 media be designed so that there is 100% transmission?

EDIT:

Do pressure waves (sound) also exhibit T.I.R.?

 

[Doc Al]

Why is it that T.I.R. only occurs when a light is traveling from a denser to a rarer medium? Intuition suggests that this should happen when going from a rarer to a denser medium. Care to get into some mathematics?

Start with Snell's law for refraction.

 

[skywalker09]

What about the physical reason? What is it about the nature of matter and light which causes this?

 

[Meir Achuz]

Also, can the interface between 2 media be designed so that there is 100% transmission?

Do pressure waves (sound) also exhibit T.I.R.?

Pressure waves also satisfy Snell's law and can have TIR.
A three media interface is needed for 100% transmission.
A "non-reflective" coating is used between the two original media.

 

[billiards]

[Sound only manifests as a pressure wave in all of its bulk when it travels through fluids - it also travels as shear waves (in solids). Sound can and does exhibit TIR, although this behaviour is limited to waves which are incident at an angle greater than the "critical angle". The so-called "sound channel" in the oceans is so-named because sound at greater than the critical angle will propagate in this layer, only able to spread its energy cylindrically, the energy travels further so is good for long distance messaging. The basic rule of thumb is that the ray will tend to be "repelled" by higher velocity media, so if you have a high velocity boundary surrounding a low velocity tube the energy will not be able to escape.