Total Internal Reflection

[nothing123]

Hi,

Let's say a question reads something like "...total internal reflection occurs when a beam of light strikes the surface of a plastic to air boundary at 45 degrees. What can you say about the n of the plastic?" My question here is, are we assuming total internal reflection JUST occurs at the 45 degrees? For if they arbitrarily just picked any angle that total internal reflection occurs at, we can't really say anything about n can we?

Thanks.

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[cwfergus]

I Think it just basically means that at 45 degrees is where total internal reflection occurs, so waht we can say is that at that point, the light must be travelling from a higher refractive index to one with a lower one. so thus, the n of the plastic must be lower than air

 

[HawkeyePostOp]

if it reflects at 45, then it definitely reflects at greater than 45.
using sin(theta) = n2/n1 where n1 > n2, we get that n1(the plastic) must have an n of at least 1.41

 

[nothing123]

Right, I guessed based on your solution, you kind of answered my question that yes, we do assume that at 45, that's when total internal reflection FIRST occurs. What I was originally trying to get at was if the question only read "...total internal reflection occurs at 45..." that doesn't mean it can't occur at something less than 45 in which case n does not have to be greater than 1.41 if you get what I'm saying in which case, we can't really say anything about n.

 

[HawkeyePostOp]

Right, I guessed based on your solution, you kind of answered my question that yes, we do assume that at 45, that's when total internal reflection FIRST occurs. What I was originally trying to get at was if the question only read "...total internal reflection occurs at 45..." that doesn't mean it can't occur at something less than 45 in which case n does not have to be greater than 1.41 if you get what I'm saying in which case, we can't really say anything about n.

If they say "critical angle" at 45 then yes, it won't occur at less than 45.
An angle that is less than 45 has to have an n greater than 1.41.
If they just say that reflection happens at this angle, all we know is the minimum value of n.