I recently visited an aquarium in Malaysia and there was a sign saying that the exhibits in their main tank appear to be smaller by 30% especially when viewed through their tunnel (https://www.youtube.com/watch?v=kiESyGtsUus; not my video).

I was wondering why would the fish appear to be smaller by 30% since water magnifies an object by 30%. Has this got to do with the curvature of the window, or the material (acrylic, by the way; refraction through three mediums)?

Can someone explain this to me?

  • $\begingroup$ Ask also if you'd like to know the math behind the "30% " decrease, then I can edit the answer to put it as a foot note. $\endgroup$ – Tausif Hossain Jul 11 '17 at 13:23

In the aquarium tunnel the fish appears smaller because the acrylic with the water behind it creates a diverging lens. You can see in the ray diagram below that fish inside the aquarium appears smaller(you outside will see a diminished or smaller virtual image). The sides of the tunnel taken approximately cylindrical( that is in the arc of a circle).

Using small angle approximations the size of the fish decreases by approximately 30%(factoring in refractive index of water and of acrylic where the refractive index of acrylic cancels out in the mathematics) if you calculate the angle of divergence. Thus the fish do appear smaller in such an arrangement for viewing in a tunnel.

Note: You can think of this scenario like the opposite of a fish bowl where fish look larger inside the bowl but here it's like you are inside the fish bowl and hence the outside world(fish in aquarium) looks smaller by the law of reversibility of light.

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