Can anyone show me a proof of "refractive index= (real depth)\(apparent depth) "?

I found the proof in my book has a mistakes and I found some contradicts to this equation.

The book said used a pair of similar triangles to infer it but the triangles are not similar.

Hope it helps you bring me out of the troubles.

Primarygun,

 

The quoted solution is not trying to prove that n = real depth/apparent depth. It is determining (although incorrectly, as pointed out) the real depth, given the apparent change in depth, and assuming that n= r.d./a.d. = 1.70

 

Do you want the correct solution to the problem (of determining the real depth) or a correct derivation of the fact that n = r.d./a.d. ? Or both ?

The flaw in the calculation above is merely in poor wording and a complete disregard to stating assumptions.

 

The rule that n = real depth / apparent depth is only an approximate rule. It is valid only when you are looking almost vertically (normally) through the interface, and hence i and r are assumed to be very small angles. In this limiting case, A is very close to P, and hence :

 

[math] AI \approx PI~;~~AO \approx PO [/math]

 

But to call the triangles similar is just ridiculous !!

n = real depth / apparent depth is only an approximate rule

Ya , I found some web sites they consider in a similar way with approximate symbol.

[math]

\approx ~

[/math]

Here I want the solution for this question as it seems to me that I've got the proof.

Thank you