Solve Refraction Problem: Aquarium Height & Diam.

  • Thread starter Gavroy
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In summary, a person with a height of 1.7m is standing in front of a cylindrical aquarium filled with water to a height of 3.9m. The diameter of the aquarium needs to be calculated, assuming the glass can be neglected. There is a grid on the top of the aquarium, but the person would be unable to see it if they crouched down due to the phenomenon of total internal reflection at the water-air interface. The question is in which angle the person needs to look up in order to see the grid.
  • #1
Gavroy
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First, I want to say sorry for my english, cause I do not live in an english-speaking country.:rolleyes:
1. Homework Statement
Here the problem definition:
There is a person which has a body height of 1.7m and is standing in front of a cylindrical aquarium, which is 4 meters high.
It is filled with water to 3.9m and on the top of it there is a grid.

Now the person is standing directly in front of the cylindrical aquarium and as soon as the person would crouche she would be unable to see the grid.
Now, one should calculate the diameter of the aquarium and it is said that the glass of the aquarium can be neglected.
I included a picture which illustrates the situation.

But there is just one person standing directly in front of the windows.

Homework Equations



I guess:
Snell's law//maybe Fresnel equations?!

The Attempt at a Solution



But I am uncertain about the question, in which angle does the person look up in order to see the grid, because if the person looks up in a 90° angle
(I assume that the person will have to look up in some way, even though it is not mentioned in the problem definition), I am not sure whether this person would see something at all, because of total reflection, of the light beam passing from the water in the air.

Maybe you could tell me your ideas(I am not expecting a complete solution).
 

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  • #2
Gavroy said:
But I am uncertain about the question, in which angle does the person look up in order to see the grid, because if the person looks up in a 90° angle
(I assume that the person will have to look up in some way, even though it is not mentioned in the problem definition), I am not sure whether this person would see something at all, because of total reflection, of the light beam passing from the water in the air.

Maybe you could tell me your ideas(I am not expecting a complete solution).
I think total internal reflection at the water-air interface is what prevents the person from seeing the grid. Draw yourself a ray diagram and see what condition must be true for a ray that starts in the middle of the grid and exits through the side of the aquarium to be reflected internally.
 

1. How do I calculate the height of an aquarium given the diameter and refraction problem?

To calculate the height of an aquarium, you will need to use the formula: height = diameter / (2 x tan(theta)). Theta refers to the angle of incidence, which can be calculated using Snell's law. First, calculate the angle of refraction using Snell's law, then use the tangent function to find the angle of incidence. Once you have the angle of incidence, plug it into the formula to calculate the height.

2. What is the formula for solving a refraction problem involving an aquarium?

The formula for solving a refraction problem involving an aquarium is height = diameter / (2 x tan(theta)). Theta refers to the angle of incidence, which can be calculated using Snell's law. Once you have the angle of incidence, plug it into the formula to calculate the height.

3. How do I determine the angle of incidence in a refraction problem involving an aquarium?

To determine the angle of incidence, you will need to use 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 indices of refraction. Rearrange the equation to solve for the angle of incidence, and then use the tangent function in the formula height = diameter / (2 x tan(theta)) to calculate the height of the aquarium.

4. What are the indices of refraction for water and glass in an aquarium?

The index of refraction for water is approximately 1.33, while the index of refraction for glass is typically around 1.52. However, these numbers may vary slightly depending on the specific type of glass and water being used in the aquarium.

5. Is there a simpler way to solve a refraction problem involving an aquarium?

There may be alternative methods for solving a refraction problem involving an aquarium, but using the formula height = diameter / (2 x tan(theta)) is generally considered the most accurate and reliable method. Other methods may involve approximations or assumptions that could affect the accuracy of the solution.

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