What is the largest theta can be if the tube is in water?

In summary, the problem involves light entering a plastic tube with a 90 degree angle and an index of refraction of 1.60. The goal is to find the largest possible angle (theta) for the light to reflect back into the tube when the corner is cut. The critical angles for air and water are 38.7 degrees and 56.2 degrees respectively.
  • #1
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Homework Statement


Light enters a solid 90 degree angled tube made of plastic having an index of refraction of 1.60. The light travels parallel to the upper part of the tube. which is horizontal You want to cut the corner of the tube so that all the light will reflect back into the tube after it strikes that face. a) what is the larget theta can be (theta is the angle from the top) if the tube is in air? b) what is the largest theta can be if the tube is in water?
*diagram attached


Homework Equations





The Attempt at a Solution


I could not find the material related to this question in the book.
 

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  • #2
You must show some work to get help on these forums. To get you started, since you said you couldn't find the material, try to read up on Snell's Law and Critical Angles.
 
  • #3
I found the critical angle, which is the largest the angle could be without total internal reflection. But the question askes what is the largest the angle can be?

I got 38.7 degrees and 56.2 degrees.
 
  • #4
nvm, i got the answer.
 

1. What is theta and how does it relate to the tube being in water?

Theta is the angle of incidence of a light ray as it enters the water. It is important in this scenario because it determines the amount of refraction that will occur as the light travels through the water and hits the tube.

2. How is the largest theta determined for a tube in water?

The largest theta can be determined by using Snell's Law, which relates the angle of incidence to the angle of refraction as the light passes through the water and hits the tube. The largest theta occurs when the angle of refraction is at its maximum, which is when the angle of incidence is 90 degrees.

3. Can the largest theta be greater than 90 degrees?

No, the largest theta cannot be greater than 90 degrees. This is because when the angle of incidence reaches 90 degrees, the angle of refraction will be at its maximum and the light will no longer be able to travel through the water and hit the tube.

4. How does the refractive index of water affect the largest theta?

The refractive index of water, which is a measure of how much the speed of light decreases as it passes through water, will affect the largest theta. A higher refractive index will result in a smaller theta, as the light will be bent more as it travels through the water.

5. Is the largest theta the same for all types of tubes in water?

No, the largest theta can vary depending on the material and shape of the tube. Different materials have different refractive indices, and the shape of the tube can also affect the angle of refraction. However, the largest theta will always occur when the angle of incidence is 90 degrees.

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