Why is refraction absent on curved surfaces?

[lalota]

Light is being a sticky unit for me, can anyone help with the following question: "Why is there no refraction at the curved surfaces?"

I've tried reseraching it, but instead I find equations of how it IS possible. Erm.. not quite answering the question. Any help appreciated, thanks!

 

[Doc Al]

Can you tell us the exact question that was asked? Curved surfaces of what? What was the context?

As you no doubt have discovered, light most definitely does refract at curved surfaces between two different media. That's how lenses work!

 

[lalota]

Well, we were conducting an investigation where we would shine a ray of light through a thick, half-circle shaped glass lying flat on a paper, and we measured the angles at which the ray refracted or reflected. When we shone the light at the straight edge of the glass, the rays refracted fine. But when we shone the light through the curved edge, there was always a total internal reflection. Then we were asked to explain why this happens.

 

[lalota]

please! -any- help would be appreciated. if I'm still not understood, i can clarify what I'm asking!

 

[paul11273]

Well, when the ray hits the first surface of the medium, it is refracted (bent). This you seem to have a handle on. When it is refracted, now it is traveling through the medium at a different angle than when it entered.
This new angle, in your situation, when combined with the angle of the curved surface, is either equal to or greater than the "critical angle" needed for internal reflection. The critical angle is simply the angle at which no light will escape the medium. This critical angle is the angle measured between the approaching ray and the normal to the surface.

theta critical = arcsin(n2/n1) where n1 > n2.

That is how to calculate the critical angle for the medium.
Where n1 and n2 are the index of refractions of the two mediums.

I hope this helps. Try calculating it, and seeing if it makes sense. I don't know if you have a copy of the traced rays so that you can measure the angle. Hopefully you have the index of refraction of the glass (or whatever the material was that you were passing the ray through) and the i of r of air is simply 1.

 

[lalota]

Thank you so much, Paul! I completely didn't think of using critical angles to explain it! Here's the answer I came up with, I would like to know if it makes sense:

"Once the light entered the glass, it was in the denser medium. In order for refraction to occur, the incidence rays must be less than the critical angle. Yet every time the light approached the glass-air boundary, it was approaching at angles greater than the critical angle. The two conditions necessary for total internal reflection were met (the light is traveling from a more dense to less dense medium, and the angle of incidence is greater than the so-called critical angle), thus all of the incident light at the curved boundary stayed internal and underwent reflection rather than refracting."

And then I included calculations for the critical angle. Any good?

 

[paul11273]

Sounds good to me. Glad that you got it now. Good luck.