On a safari, you are spear fishing while wading in a river. You observe a fish g

Question

On a safari, you are spear fishing while wading in a river. You observe a fish gliding by you. If your line of sight to the fish is 66.0degree below the horizontal in air, and assuming the spear follows a straight-line path through the air and water after It is released, determine the angle below the horizontal that you should aim your spear gun in order to catch dinner. Assume the spear gun barrel is 1.60 m above the water surface, the fish is 1.30 m below the surface, and the spear travels in a straight line all the way to the fish. A point source of light is located 3.6 in below the surface of a large pool of water. Find the area of the largest circle on the pool's surface through which light coming directly from the source can emerge. m^2

Explanation / Answer

Q3.

consider the scenario when light from the fish crosses the water-air interface.

let angle of incidence be theta degrees.

angle of refraction =90-66=24 degrees

(as your line of sight is obtained by extending the refracted ray backwards into water)

refractive index of air is 1 and water is 1.33

so using snell's law:

1*sin(24)=1.33*sin(theta)

==>theta=17.807 degrees

so angle below horizontal to which you should aim for is given by 90-17.807=72.193 degrees

Q4.

we need to find critical angle for total internal reflection

in this case,

angle of incidence let be theta.

angle of refraction=90 degrees

then using snell's law:

1.33*sin(theta)=1*sin(90)

==>theta=48.7534 degrees

so for an angle upto 48.7534 degrees, the light source can emerge from the pool surface.

so if distance of the source for this angle is r,

then tan(48.7534)=r/3.6

==>r=4.1055 m

so area of the largest circle=pi*r^2

=52.9523 m^2

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