Maximum Angle for Total Internal Reflection

In summary, the maximum value of θ1 that would cause total internal reflection to occur is 22.6 degrees, with indices of refraction N1 = 1.3 and n2 = 1.6. The critical angle is found using the equation sin^-1(n1/n2) and in this case, the ray reflects off the N2/N3 border. To find θ1, first calculate θ2 and then use it to find θ1.
  • #1
Tekee
20
0

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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  • #2
Post the diagram.
 
  • #3
Oops, it's attached now.
 

Attachments

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  • #4
The diagram shows three layers. What are their indices? Where is the total internal reflection supposed to take place?
 
  • #5
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.
 
  • #6
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.
 
  • #7
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:
 
  • #8
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.
 

1. What is total internal reflection?

Total internal reflection is a phenomenon that occurs when a light ray traveling through a medium reaches a boundary with a less dense medium at an angle greater than the critical angle. In this scenario, the light ray is completely reflected back into the same medium, instead of being refracted into the less dense medium.

2. What causes total internal reflection to occur?

Total internal reflection occurs due to the change in speed of light when it travels from one medium to another. When light travels from a denser medium to a less dense medium, it slows down and bends away from the boundary. If the angle of incidence is large enough, the light ray will be completely reflected back into the denser medium.

3. What is the critical angle in total internal reflection?

The critical angle is the angle of incidence at which total internal reflection occurs. It is dependent on the refractive indices of the two mediums involved. The larger the difference in refractive indices, the smaller the critical angle will be.

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

Total internal reflection is used in various applications such as fiber optics, prisms, and mirages. In fiber optics, total internal reflection is used to transmit light signals through thin fibers, allowing for high-speed and long-distance communication. Prisms use total internal reflection to split white light into its component colors. Mirages are created when light rays undergo total internal reflection in hot air near the ground, creating the illusion of water on a hot road.

5. Can total internal reflection occur in all mediums?

No, total internal reflection can only occur when light travels from a denser medium to a less dense medium. It is not possible for total internal reflection to occur when light travels from a less dense medium to a denser medium, as the light will always be refracted away from the boundary.

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