Solve Snell's Law: Glass Cube Refractive Index = 1.77

In summary, the glass in this scenario has a refractive index of 1.77, which means that light is not refracted into the water when it is incident at an angle greater than 48.7 degrees from the normal.
  • #1
DylanXO
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Homework Statement


A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass-water interface at an angle to the normal greater than 48.7°, no light is refracted into the water. Calculate the refractive index of the glass.

Homework Equations


Snell's Law:
snells_law_formula_2.png

Refractive Index of Water: 1.33

The Attempt at a Solution


Na = Nb*Sin(Θb)/Sin(Θa)
Na = 1.33*Sin(90°)/Sin(48.7°)
Na = 1.77
Glass Cube Refractive Index = 1.77

I feel that I have made an error or that I'm not grasping the concept correctly. Any guidance or explanation would be highly appreciated.
 

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  • #2
No, it looks right to me. What makes you think it isn't?
 
  • #3
This looks good to me. This phenomenon is called total internal reflection, in case you want to explore it a bit.
 
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  • #4
DylanXO said:
...I feel that I have made an error or that I'm not grasping the concept correctly...

Seems correct to me as well. glasses refractive indices are typically around that value. Any part of the concept you are confused about?
 
  • #5
Doc Al said:
This looks good to me. This phenomenon is called total internal reflection, in case you want to explore it a bit.
Thank you, I think some additional reading on that will help resolve any confusion I'm having.
 
  • #6
renec112 said:
Seems correct to me as well. glasses refractive indices are typically around that value. Any part of the concept you are confused about?
It was more the result itself from textbooks I have checked and a quick look online, it seemed that the indices for glass were lower. Although I understand now, that the indices for glass are varying.
 
  • #7
The incidence angle 48.7º in this case, is the critical angle, i.e, the angle which makes the refraction angle 90º. We know that because in the statement of the problem, we can read the following:

[..] You find that if the ray is incident on the glass-water interface at an angle to the normal greater than 48.7°, no light is refracted into the water.

The fact that for any angle greater than 48.7º no light is refracted into the water, means that 48.7º is the critical angle and the refraction angle is 90º.

That is the reason you have used 90º into the Snell's Law.

Reference: https://en.wikipedia.org/wiki/Total_internal_reflection
 
  • #8
DylanXO said:
It was more the result itself from textbooks I have checked and a quick look online, it seemed that the indices for glass were lower. Although I understand now, that the indices for glass are varying.
I forgot i once made this animation about it:

It's showing a light ray going from water (bigger index) to air(lower index) - an example where internal reflection can happen.
 
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  • #9
renec112 said:
I forgot i once made this animation about it:

It's showing a light ray going from water (bigger index) to air(lower index) - an example where internal reflection can happen.
Amazing animation, thanks for share!
 
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Related to Solve Snell's Law: Glass Cube Refractive Index = 1.77

What is Snell's Law?

Snell's Law, also known as the law of refraction, is a formula that describes the relationship between the angle of incidence and the angle of refraction when a light ray passes through two different mediums.

How do you solve Snell's Law?

The formula for Snell's Law is n₁sinθ₁ = n₂sinθ₂, where n₁ and n₂ are the refractive indices of the two mediums and θ₁ and θ₂ are the angles of incidence and refraction, respectively. In order to solve for any of these variables, you need to know the values of the other three and plug them into the formula.

What is the refractive index of glass?

The refractive index of glass varies depending on the type of glass, but on average it is around 1.5. However, in this specific case, the refractive index of the glass cube is given as 1.77.

How does the refractive index affect the bending of light?

The refractive index of a medium determines how much a light ray will bend when passing through it. The higher the refractive index, the greater the bending of light. This is because the refractive index is a measure of how much slower light travels through a medium compared to a vacuum.

Why do different mediums have different refractive indices?

The refractive index of a medium is determined by its optical density, which is a measure of how much light is slowed down as it passes through the medium. Different materials have different optical densities, thus resulting in different refractive indices.

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