Reflection and Refraction, much index of refraction

In summary, Glass has a higher index of refraction than water, therefore light will refract more when traveling from glass to water.
  • #1
davidelete
28
0

Homework Statement


1. The index of refraction for water is 1.33 and that of glass is 1.50.

a. What is the critical angle for a glass-water interface?b. In which medium is the light ray incident for total internal reflection?

Homework Equations


nisin[tex]\vartheta[/tex]i=nrsin[tex]\vartheta[/tex]r

The Attempt at a Solution


a. I think the answer to a. is 62.46 degrees, but I am not sure.
b. I think the answer is glass, simply because it is going to be moving from a less dense area to a more dense area.
 
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  • #2
Use Snell's law:

[tex]n_1\sin\theta_1 = n_2\sin\theta_2\ .[/tex]

Note: It's not additive like you suggested.

At the critical angle, [tex]\theta_2[/tex] is 90 degrees (the light refracts along the boundary). That is to say, it's sin is 1. We can therefore rearrange for the critical angle:

[tex]\theta_{\mathrm{crit}} = \sin^{-1} \left( \frac{n_2}{n_1} \right)[/tex]

Now we have two refractive indices, the glass and the water. If you plug them in incorrectly, you're going to end up with trying to find the inverse sin of a value > 1, which isn't possible as this has no solution.
 
  • #3
astrorob said:
Use Snell's law:

[tex]n_1\sin\theta_1 = n_2\sin\theta_2\ .[/tex]

Note: It's not additive like you suggested.

At the critical angle, [tex]\theta_2[/tex] is 90 degrees (the light refracts along the boundary). That is to say, it's sin is 1. We can therefore rearrange for the critical angle:

[tex]\theta_{\mathrm{crit}} = \sin^{-1} \left( \frac{n_2}{n_1} \right)[/tex]

Now we have two refractive indices, the glass and the water. If you plug them in incorrectly, you're going to end up with trying to find the inverse sin of a value > 1, which isn't possible as this has no solution.

Quite sorry for the mistake in Snell's Law. I knew what it meant, I just messed up when writing it in the forum.

Anyway, I appreciate the input, but if you are using
[tex]\theta_{\mathrm{crit}} = \sin^{-1} \left( \frac{n_2}{n_1} \right)[/tex], would it not be possible to put 1.33 (n2) over 1.5 (n1)? This would look like
[tex]\theta_{\mathrm{crit}} = \sin^{-1} \left( \frac{1.33}{1.5} \right)[/tex] and if plugged into a calculator, would return 62.45732485 degrees.
 
  • #4
For this problem I calculated 62.4 degrees, the same thing you got.

As for B, I put water.
 
  • #5
Yes, that's correct as you've stated.

It also gives you the answer to your second question as [tex]n_2[/tex] represents the refractive index of the medium that the light traveling in medium [tex]n_1[/tex] is incident on.
 
  • #6
patriots1049 said:
For this problem I calculated 62.4 degrees, the same thing you got.

As for B, I put water.

Ah, thank you. I was actually thinking that it would be glass because my book details the fact that "Total internal reflection occurs when light passes from a more optically dense medium to a less optically dense medium at an angle so great that there is no refracted ray." This would mean that glass-water would be a more optically dense to a less optically dense scenario.
 
  • #7
astrorob said:
Yes, that's correct as you've stated.

It also gives you the answer to your second question as [tex]n_2[/tex] represents the refractive index of the medium that the light traveling in medium [tex]n_1[/tex] is incident on.

Thank you very much. You have been a big help today, astrorob.
 

Related to Reflection and Refraction, much index of refraction

1. What is the difference between reflection and refraction?

Reflection is the bouncing back of light when it hits a surface, while refraction is the bending of light as it passes through a medium with a different index of refraction.

2. How is the index of refraction determined for a material?

The index of refraction is determined by the speed of light in a vacuum divided by the speed of light in the material. This value represents how much the light is slowed down as it passes through the material.

3. What factors affect the index of refraction of a material?

The index of refraction is affected by the density and composition of the material, as well as the wavelength of the light passing through it. Temperature and pressure can also impact the index of refraction.

4. How does the index of refraction affect the behavior of light?

The index of refraction determines how much light is bent or refracted as it passes through a material. A higher index of refraction means that light will be bent more, while a lower index of refraction means that light will be bent less.

5. Why do objects appear distorted when viewed through a curved surface?

When light passes through a curved surface, such as a lens, it is refracted at different angles, causing the object to appear distorted. This is due to the varying thickness and index of refraction throughout the curved surface.

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