Calculating Real Depth Without Given Angles: Applying Snell's Law

In summary, the question is about finding the real depth of a coin in a water-filled container using Snell's Law. The angles of incidence and refraction are not given, so the person asking is unsure how to apply the law. They suggest using trigonometric approximations and experimenting with different angles to find a range that would work.
  • #1
Perpendicular
49
0
Hi all, I have this problem :

A coin is dipped to the bottom of a water filled container made of an opaque material. Observed from the water surface, the depth of the coin appears to be 2 meters. Find the real depth ( R.I. of water = 1.33 )

Since angles are not given, how do I apply snell's law here ? I would normally find the tangent values of angles of incidence and refraction but as angles are not given, I cannot derive the real depth that way. Sines are not helping here. See attached diagram for reference ( MSPaint work, so might be bad ) - snell's law allows me to find the ratio of CD and BD. After that, I can't do anything.

[PLAIN]http://img638.imageshack.us/img638/4082/38043092.png
 
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  • #2
Hint: Consider that you are observing the coin from almost directly above. So the angles of incidence and refraction are small.
 
  • #3
How'd that help, exactly ? What difference does that make ?
 
  • #4
Perpendicular said:
How'd that help, exactly ? What difference does that make ?
sinθ ≈ tanθ, for one.
 
  • #5
Doc Al said:
sinθ ≈ tanθ, for one.

Surely such approximations would lead to slight inaccuracies. What angular ranges are we talking about ?
 
  • #6
Play around with some angles and see.
 
  • #7
I would if you suggested me a range .
 

Related to Calculating Real Depth Without Given Angles: Applying Snell's Law

What is real and apparent depth?

Real and apparent depth are concepts used to describe the perceived distance between objects in space. Real depth refers to the actual physical distance between two objects, while apparent depth is the apparent distance between the same two objects as perceived by an observer.

What is the difference between real and apparent depth?

The main difference between real and apparent depth is that real depth is the actual distance between two objects, while apparent depth is the perceived distance between the same two objects. This means that real depth is a measurable and objective value, while apparent depth is subjective and can vary from person to person.

How is real and apparent depth related to refraction?

Real and apparent depth are closely related to refraction, which is the bending of light as it passes through different mediums, such as air and water. When light travels through a medium with a different optical density, the path of the light is bent, resulting in a change in the apparent depth of an object.

What factors affect the perception of real and apparent depth?

The perception of real and apparent depth can be affected by various factors, including the distance between objects, the angle of view, and the presence of atmospheric conditions (such as fog or haze). Additionally, individual differences in vision and perception can also impact the perception of depth.

How is real and apparent depth used in scientific research?

Real and apparent depth are important concepts in scientific research, particularly in the fields of optics and vision. They are used to understand how light behaves and how the human brain processes visual information. These concepts are also applied in various fields such as astronomy, microscopy, and virtual reality technology.

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