Hiding behind a goldfish

Classical Mechanics Level 4

Things can be made invisible in one direction using a combination of lenses and mirrors which would bend the light around them. One way to hide a certain area is to build a big aquarium with water as shown in the picture that will bend the light.

What should be the width X of the aquarium in m so that we can hide \(1~\mbox{m}\) of space? \(1~\mbox{m}\) of space means the distance between the outgoing light rays in the figure is 1 m.

Details and assumptions

  • The refractive index of water is \(1.33\).
  • The prism angle \(\alpha\) of the aquarium is \( 30^\circ\).

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