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. Assuming that the ring is small enough compared to the depth of the river to be treated as a point and that the Rhine is 10.0 m deep where the ring goes in, 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?

Short answer

Area of the largest circle at the surface of the water

Step-by-step solution

Snell’s law

Snell's law determines the degree of refraction as well as the relationship between the angle of incidence, angle of refraction, and refractive indices of two media.

Here;

Critical Angle-Beyond which light rays traveling through a thicker media to the surface of a less dense medium are no longer refracted but completely reflected

Total Internal Reflection-When the angle of incidence surpasses the critical angle, a light ray reaches an interface with less dense material and is completely reflected.

Area of the largest circle at the surface of the water

When theta exceeds the critical angle, the ray is reflected into the water once more. As a result, the biggest circle will be formed when the angle equals the critical angle.

Medium 1 is water

Medium 2 is air

So, critical angle is;

Area of the largest circle at the surface of the water;

Area of the largest circle at the surface of the water