Maximum Angle for Total Internal Reflection

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Homework Help Overview

The problem involves determining the maximum angle for total internal reflection, given two refractive indices (N1 = 1.3 and N2 = 1.6) and a third index (N3 = 1.2) that may be relevant to the setup. The original poster expresses uncertainty about the critical angle concept and its application in this context.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the critical angle and questions whether their understanding of the relationship between angles and total internal reflection is correct. Other participants inquire about the indices of refraction and the specific layers involved in the reflection process.

Discussion Status

The discussion is ongoing, with participants clarifying the layers involved and the indices of refraction. Some guidance has been offered regarding the need to find angles in relation to the layers, but no consensus or resolution has been reached yet.

Contextual Notes

There is some confusion regarding which layers are relevant for the total internal reflection and how the indices of refraction apply to the problem setup. The original poster has expressed a lack of confidence in their understanding of the critical angle.

Tekee
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Homework Statement



What is the maximum value of θ1 that would cause total internal reflection to occur? N1 = 1.3, n2 = 1.6 (picture attached)

Homework Equations



Critical angle = sin^-1(n1/n2)

The Attempt at a Solution



I figured the critical angle to be 54.3. That means that theta1 has to be less than 35.7 degrees in order for total internal reflection to occur, correct? However, the answer that I am supposed to get is 22.6 degrees.

I am interested in seeing how this problem works out, but I'm also a bit shaky on the critical angle concept. Thanks for the help!
 
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Post the diagram.
 
Oops, it's attached now.
 

Attachments

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The diagram shows three layers. What are their indices? Where is the total internal reflection supposed to take place?
 
Only the top two layers are used in this problem. The ray is coming from layer 1 and reflecting off layer 2.

I posted the indices in my first message.
 
Tekee said:
Only the top two layers are used in this problem. The ray is coming from layer 1 and reflecting off layer 2.
But total internal reflection takes place when light reflects off a layer with a lower index of refraction.
 
N3 is 1.2, if that helps. In this case, then, I would assume that the ray bounces off the N2/N3 border. Sorry for the confusion! You can see that I don't really have a grasp on the topic :blushing:
 
Tekee said:
N3 is 1.2, if that helps. In this case, then, I would assume that the ray bounces off the N2/N3 border.
That makes more sense. So give it a second try. First find θ2, then use it to find θ1.
 

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