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

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Homework Help Overview

The problem involves determining the real depth of a coin submerged in water, given its apparent depth and the refractive index of water. The challenge arises from the lack of provided angles for applying Snell's Law effectively.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply Snell's Law but struggles due to the absence of angle measurements. Some participants suggest considering the observation angle to simplify the problem, while others question the implications of such approximations.

Discussion Status

Participants are exploring the relationship between angles and the application of Snell's Law, with some guidance offered regarding the observation angle. However, there is no consensus on how to proceed without specific angle values, and the discussion remains open-ended.

Contextual Notes

There is a mention of potential inaccuracies due to approximations, and participants are considering the implications of angular ranges in their reasoning.

Perpendicular
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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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Hint: Consider that you are observing the coin from almost directly above. So the angles of incidence and refraction are small.
 
How'd that help, exactly ? What difference does that make ?
 
Perpendicular said:
How'd that help, exactly ? What difference does that make ?
sinθ ≈ tanθ, for one.
 
Doc Al said:
sinθ ≈ tanθ, for one.

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

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