Maximum Angle for Total Internal Reflection

[Tekee]

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!

 

[Doc Al]

Post the diagram.

 

[Tekee]

Oops, it's attached now.

 

[Doc Al]

The diagram shows three layers. What are their indices? Where is the total internal reflection supposed to take place?

 

[Tekee]

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.

 

[Doc Al]

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.

 

[Tekee]

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

 

[Doc Al]

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.