Answer :
The angle from the vertical does the fish see the top of the fishermans head is 42.24 degrees and can be finded out by snells law.
According to Snell’s Law when light is incident on an interface separating two media, the angles of incidence and refraction, θ1 and θ2, are related,
n1 sin(θ1) = n2 sin(θ2)
where θ1 or θ2 is the angle between the normal to the interface and the direction in which incident or refracted wave is propagating. The quantities n1 and n2 are the indices of refraction of the two media.
While the speed of light is constant in a vacuum, the speed of light in air and in transparent solids is somewhat less. The ratio of the speed of light in a vacuum (c) to the speed of light in a solid (v) is called the index of refraction (n) of the solid.
Applying snells law,
nwater *sinα = nair *sinβ
nwater *sinα = sinβ
sinα = sinβ/nwater
sinβ = 1.33 sinα
AB = 3.5m-BC
AB = 3.5m-CDtanβ
AB = 3.5m-1.55*tanβ
Also, AB = 4.5m*tandα
4.5m*tandα = 3.5m-1.55*tanβ
4.5m*tandα = 3.5m-1.55*(sinβ/cosβ)
4.5m*tandα = 3.5m-1.55*1.33sinα/[tex]\sqrt{1-(1.33)^2*(sin\alpha )^2}[/tex]
α=42.24 degrees.
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