A 1.55-m tall fisherman stands at the edge of a lake, being watched by a suspici

Question

A 1.55-m tall fisherman stands at the edge of a lake, being watched by a suspicious trout that is 3.50 m from the fisherman in the horizontal direction and 45 cm below the surface of the water. a. Sketch a diagram of the problem. b. At what angle from the vertical does the fish see the top of the fisherman’s head?

Can someone PLEASE answer this thoroughly so that I don't have to keep posting the same question to get help. Please show ALL steps, even the algebraic work, because I am not following all of the previous answers posted.

Correct answer is roughly 42-43 degrees but I cannot figure out how. Please show steps that do NOT result in multiple equations.

It is suggested we visit this site as a reference for setting up this problem: http://www.physicstutorials.org/home/optics/refraction-of-light/apparent-depth-real-depth

Explanation / Answer

By snells law, we have n1 sini1 = n2 sini2

for air, n = 1, for water n=1.33. Let refraction takes place at a distance x from edge

X/sqrt(1.55^2 +x^2) = 1.33×(3.5-x)/sqrt(0.45^2+ (3.5-x)^2)

By hit and trial method if x=3,

LHS= 0.888

RHS = 0.988 it means x is even more

If x = 3.15m

LHS =0.897

RHS=1.33× 0.35/ sqrt{.35^2 +.45^2}=0.816

So x =3.08 m approximately,

Angle at which fish sees, = tan-1(3.08/1.55)

Angle is 63.3 degree with vertical

sorry but I dont think 42-43 degree is feasible with the given value

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