Maximum critical angle for total reflection?

In summary, this problem is quite simple to solve, but it can be more complicated if you want to find pheta2 for different pheta1s. Sinpheta critical = n2/n1 (as long as n1 is greater than n2) If pheta1 = critical angle, then pheta2 should be 90 degrees. However, for the total reflection angle, refraction angle, and pheta2, you may not be able to use snells law.
  • #1
shangriphysics
32
1

Homework Statement


A beam of light is incident on the boundary between a piece of glass to air. The index of refraction of the piece of glass is 1.4. Find the critical angle.

It is quite simple to figure out this problem. Sinpheta critical = n2/n1 (as long as n1 is greater than n2)

However, let say I wanted to find pheta 2, with different pheta1s. Since I know the critical angle, I know that if pheta1 = critical angle, then pheta2 should be 90 degrees.

When I double check using snells law I do not seem to get 90 degrees. Can I even use snells law in these scenarios to find pheta2, for the total reflection angle, refraction angle?

I also know if pheta 1 is less than pheta2 refraction will occur, and if pheta1 is greater than the critical angle, total internal reflection will occur.
 
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  • #2
shangriphysics said:
A beam of light is incident on the boundary between a piece of glass to air. The index of refraction of the piece of glass is 1.4. Find the critical angle.

It is quite simple to figure out this problem. Sinpheta critical = n2/n1 (as long as n1 is greater than n2)

However, let say I wanted to find pheta 2, with different pheta1s. Since I know the critical angle, I know that if pheta1 = critical angle, then pheta2 should be 90 degrees.

When I double check using snells law I do not seem to get 90 degrees. Can I even use snells law in these scenarios to find pheta2, for the total reflection angle, refraction angle?

What do you mean on pheta 2?

Show what you get for the angle of refraction when the angle of incidence in glass is equal to the critical angle.

ehild
 
  • #3
Pheta 2 is the angle that light makes after it either reflects or refracts in respect to the normal line.

1.4Sin(45)=1Sin(?) Where 1.4 is n1 and some medium, and 1 is n2 which is the air.

I will get 81.86 degrees for angle 2(pheta2)
 
  • #4
45° is less than the critical angle. You get the critical angle θc if pheta2 =90°.

1.4 sinθc= sin90° = 1. What is θc?

ehild
 
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  • #5
Thank you Ehild! I see now. I can use snells law!
 
  • #6
shangriphysics said:
I see now. I can use snells law!

Of course you can use it! :smile:

ehild
 

Related to Maximum critical angle for total reflection?

1. What is the maximum critical angle for total reflection?

The maximum critical angle for total reflection is the angle at which a light ray is incident on a boundary between two materials, and the angle of refraction is exactly 90 degrees. This results in all of the light being reflected back into the original material, with none being transmitted into the second material.

2. How is the maximum critical angle for total reflection calculated?

The maximum critical angle for total reflection can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials. The maximum critical angle can be found by setting the angle of refraction to 90 degrees.

3. What factors affect the maximum critical angle for total reflection?

The maximum critical angle for total reflection is affected by the refractive indices of the two materials at the boundary, as well as the wavelength of the incident light. It is also influenced by the surface roughness and the angle of incidence of the light.

4. What is the relationship between the maximum critical angle and the angle of incidence?

The maximum critical angle and the angle of incidence have an inverse relationship. As the angle of incidence increases, the maximum critical angle decreases. This means that at higher angles of incidence, there is a greater chance of total reflection occurring.

5. What practical applications does the maximum critical angle for total reflection have?

The maximum critical angle for total reflection is used in various optical devices such as prisms and optical fibers to reflect light and guide it through different mediums. It is also used in techniques such as total internal reflection fluorescence microscopy to observe biological samples at a high resolution. Additionally, it is utilized in the design of anti-reflective coatings for lenses and windows to reduce glare and improve visibility.

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