Total internal reflection question

In summary, the conversation discusses the relationship between the angle of incidence and the angle of reflection after the critical angle in total internal reflection. The equation n1 sin(theta1) = n2 sin(theta2) breaks down after the critical angle, resulting in total internal reflection. The person in the conversation is looking for a relation between the angle they are looking at the surface and the angle of the reflecting ray. The response is that the law of reflection still applies, even in cases of total internal reflection.
  • #1
student85
138
0
How do the angle of incidence relate mathematically with the angle of reflection after the critical angle, that is, in a TIR?
Say we have a person standing at the bottom of a swimming pool, if we take the n for water as 1.33 and for air as 1, we get the critical angle of 48.75 degrees. When the person sees the surface of the water that's further away, the angle of incidence (eye to surface) increases, but how does the other angle change?
The equation n1 sin(theta1) = n2 sin(theta2) doesn't seem to work anymore when the criticle angle is passed...
 
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  • #2
It's not clear what your question is. The last sentence you wrote is the whole point of T.I.R. Indeed, the equation breaks down because sine can't be > 1. Which means that there is NO transmitted ray (hence total internal reflection). If you have already calculated the criticAL angle, then the only part of the problem that remains is the qualitative question. What happens when the person looks a the surface of the water at a point far away from him (in the direction // to the surface) rather than at the point directly above him?
 
  • #3
Yeah I know, but what I want is a relation between the angle the person is looking by to the surface and the angle of the reflecting ray. I don't know if I'm making myself clear...

Once the critical angle is passed, how do you relate the angles?
 
  • #4
student85 said:
Yeah I know, but what I want is a relation between the angle the person is looking by to the surface and the angle of the reflecting ray.

Oh, the reflecting ray? The totally internally reflected ray still obeys the law of reflection:

angle of incidence = angle of reflection

Look at a proof of this law, and you'll that there's no reason why it wouldn't also be true at an interface where a ray is (in general) partially reflected and partially transmitted.
 
  • #5
Thanks, I was thinking that but somehow something didn't make sense.
Thank you.
 

What is total internal reflection?

Total internal reflection is a phenomenon that occurs when a light ray traveling through a medium with a higher refractive index reaches a boundary with a medium of lower refractive index at an angle greater than the critical angle. In this scenario, all of the light is reflected back into the original medium instead of being refracted into the second medium.

What is the critical angle?

The critical angle is the angle of incidence at which total internal reflection occurs. It is determined by the refractive indices of the two mediums and can be calculated using Snell's Law.

What are some real-life applications of total internal reflection?

Total internal reflection is used in various optical devices such as prisms, fiber optics, and optical fibers. It is also utilized in diamond cutting and mirages in nature.

Is total internal reflection only possible with light?

No, total internal reflection can also occur with other types of waves, such as sound waves, water waves, and radio waves. However, it is most commonly studied and observed in the context of light waves.

What factors can affect the critical angle?

The critical angle is affected by the difference in refractive indices between the two mediums, as well as the wavelength of the incident light. It can also be altered by changes in temperature or pressure of the mediums.

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