At the very end of Wagner\'s series of operas Ring of the Nibelung, Brünnhilde t
ID: 2023052 • Letter: A
Question
At the very end of Wagner's series of operas Ring of the Nibelung, Brünnhilde 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.A) 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 12.6 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.
Explanation / Answer
Snells law:
N1 sin(@c) = N2 sin (@t)
N1=water= 1.333
N2=air=1
@t = 90 due to total internal reflection
@c = unknown
(4/3)sin@=1*1
@= inverse sign .75
@ is the critical angle = 48.6 degrees.
You should now have a triangle.
You know the depth (12.6m) and you know the top angle (48.6)
Tan(@)= opposite/adjacent
Tan(48.6) * 12.6 m = opposite or x-axis component.
= 14.29m
If you parallel this to the surface of the river, you have a radius.
Area=pi r *2
Area = 3.14 *(14.29)^2
Area ~ 641.2 m^2
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