At the very end of Wagner\'s series of operas Ring of the Nibelung, Brunnhilde t

Question

At the very end of Wagner's series of operas Ring of the Nibelung, Brunnhilde takes the golden ring from the finger of the dead Siegfried and throws it into the Rhine, where it sinks to the bottom of the river. Assuming that the ring is small enough compared to the depth of the river to be treated as a point and that depth of the Rhine where the ring goes in is 13.5 m , what is the area of the largest circle at the surface of the water over which light from the ring could escape from the water? Use 1.33 for the index of refraction of water. A =

Explanation / Answer

Here,

depth of ring , h = 13.5 m

refractive index of water , n = 1.33

for the maximum angle of refraction in water

using snells law

n1 * sin(r) = 1 * sin(90)

1.33 * sin(r) = 1

r = 48.75 degree

Now , the radius of circle will be

R = h * tan(r)

R = 13.5 * tan(48.75)

R = 15.4 m

area of circle , A = pi * R^2

A = pi * 15.4^2

A = 744.4 m^2

the area of largest circle is 744.4 m^2

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