Equation of refractive index./

[Primarygun]

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.

[DQW]

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 ?

[DQW]

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 !!

[Primarygun]

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