Critical angle (symmetry of refraction) confusion

• Glenn G
In summary, refraction has a symmetry where light going from glass to air refracts away from the normal. This can be seen in diagrams of total internal reflection, where there is always a reflected ray in the more dense medium. After the critical angle, all the energy is reflected. This can be easily understood by searching "total internal reflection" on Google and looking at correct diagrams.
Glenn G

Refraction has a symmetry; on going from glass to air light at the glass air surfaces refracts away from the normal. If you turn the light source around and make the former refracted beam the incident beam then its refracted angle will be the former incident angle. So at critical angle, do the same trick, skim the light along the surface. how does it know what to do? carry on skimming or refract into the glass at 41.8 degrees.

what then troubled me even more is that if a beam skimming the surface can spontaneously refract into the glass the why doesn't light refracted at 90 degrees (due to i being critical) refracted back in again .

Does this mean that the whole idea of a critical angle is a limiting idea ... if below critical light refracts out the block, if incident angle is above the critical we get TIR - so what actually happens at the boundary between these two?

I think you have it right, that it is a limit type of behavior as the critical angle is approached. The reflectivity is high, near unity, as the light skims the surface on the air side. Measuring a precise angle of refraction becomes more difficult, as the incident beam skims the surface.

Glenn G
Notice that there is no real discontinuity here however. Why would you expect the glancing beam to suddenly snap to 90 deg?
Only a 0deg entrant beam exits at 0 deg. The angles and intensities are smooth functions. I guess "total internal reflection" is a bit surprising.
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Glenn G
Yeah, still baffled by the skimming on the surface reality. Feels like we've either got refraction away or reflection off but if you drill at the interface between refraction away and reflection don't think you can wave the 90% refracted angle away. Refracted angle is clearly approaching 90 degrees as i is increasing and at some point we do get TIR ... both frustrated and fascinated by this in equal measure

I think you have it right, that it is a limit type of behavior as the critical angle is approached. The reflectivity is high, near unity, as the light skims the surface on the air side. Measuring a precise angle of refraction becomes more difficult, as the incident beam skims the surface.
Sorry I meant the glancing beam starts to refract in at 41.8 degrees - if we reverse the arrows in the above diagram

Glenn G said:
Summary:: Incident light at the critical angle produces a refracted angle of 90 degrees. (e.g. 41.8 degrees in n=1.5). Heard it said 'light skims across the surface'. So if you reverse the direction and shine light in at 90 degrees, does it refact at 41.8 and how would it now how to do this?

Refraction has a symmetry; on going from glass to air light at the glass air surfaces refracts away from the normal.
This frequently confuses people.
You have missed out a very important ray in your diagram where the ray goes through the surface. There is always a reflected ray, in the more dense medium. (Whatever the incident angle - even normal)
It's just that, after the critical angle, all the energy is reflected.

Google search Total Internal Reflection and you will see hundreds of correct versions of the diagram. No point in my drawing it.

There is also a reflected ray when the light is incident from the air!

1. What is critical angle and how does it relate to symmetry of refraction?

Critical angle is the angle at which light passes through a boundary between two mediums and is no longer refracted, but instead is reflected back into the original medium. This angle is important because it marks the point where total internal reflection occurs, creating a symmetrical pattern of light.

2. How is critical angle calculated?

Critical angle can be calculated using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two mediums. The critical angle is then the angle of incidence at which the angle of refraction becomes 90 degrees.

3. What factors affect the critical angle?

The critical angle is affected by the refractive indices of the two mediums, with a larger difference in refractive indices resulting in a smaller critical angle. The wavelength of light also plays a role, with shorter wavelengths having a smaller critical angle. The surface roughness of the boundary can also affect the critical angle.

4. Can critical angle be observed in everyday situations?

Yes, critical angle can be observed in everyday situations such as when light passes from water to air at the surface of a pond or swimming pool. The critical angle is also important in fiber optics, where it allows for the transmission of light signals through the fiber without significant loss of light.

5. How does critical angle relate to the concept of total internal reflection?

Critical angle is directly related to total internal reflection. When the angle of incidence is greater than the critical angle, total internal reflection occurs and the light is reflected back into the original medium. This phenomenon is used in many practical applications, such as in optical fibers and prisms.

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