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

[Perpendicular]

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

 

[Doc Al]

Hint: Consider that you are observing the coin from almost directly above. So the angles of incidence and refraction are small.

 

[Perpendicular]

How'd that help, exactly ? What difference does that make ?

 

[Doc Al]

How'd that help, exactly ? What difference does that make ?

sinθ ≈ tanθ, for one.

 

[Perpendicular]

sinθ ≈ tanθ, for one.

Surely such approximations would lead to slight inaccuracies. What angular ranges are we talking about ?

 

[Doc Al]

Play around with some angles and see.

 

[Perpendicular]

I would if you suggested me a range .