Why fish under water see a circle surrounded by darkness

[Drezzan]

A fish looking straight up to the surface of a pond receives a cone of light filled with images. This bright field is surrounded by darkness. Explain what is happening and compute the cone angle.

No given data but $n_w=1.33$

No give equations but I anticipate Snell's law and maybe the critical angle equations will come into play.My attempts were to explain this by the light rays being bent in a way that the higher $\theta_i$ completely miss the fish eye. However that would not create the dark halo effect the problem states. I have looked for an answer using total internal reflection but that requires the light to be passing from a dense medium to a less dense. Total external reflection also has the stipulation the that the frequency of the light must be much greater than the resonant frequency of the atoms, and this would cause no light transmitted correct? Please help me understand this question a bit better. Thank you !

 

[Antiphon]

"I have looked for an answer using total internal reflection but that requires the light to be passing from a dense medium to a less dense"

So what would this look like to you if you were underwater? Assume that there is only darkness from the direction of the water and all the light is coming from above the water.

 

[marty1]

outside of that cone, there is reflection only of the "darkness" from below.

 

[Drezzan]

Oh wow thank you I guess I was over thinking this.

 

[paranormal]

Thank you for your question. The phenomenon you are describing is known as the "fish eye effect" and it is a result of refraction and total internal reflection of light at the air-water interface.

When light travels from one medium to another, such as from air to water, it changes speed and direction due to the difference in the refractive index of the two mediums. In this case, light travels slower in water than in air, causing it to bend or refract as it enters the water.

As the light enters the water, it spreads out in all directions, creating a cone of light. This cone of light fills the fish's field of view, allowing it to see the surrounding images. However, as the light travels through the water, it also undergoes total internal reflection at the air-water interface. This is because the angle of incidence of the light is greater than the critical angle, causing all the light to be reflected back into the water.

This results in a dark halo or ring around the cone of light that the fish sees. The cone angle can be calculated using Snell's law and the critical angle equation, as you mentioned. The exact angle will vary depending on the refractive index of the water and the angle at which the fish is looking up to the surface.

In summary, the fish sees a circle surrounded by darkness because of the refraction and total internal reflection of light at the air-water interface. This phenomenon is important for the survival of fish as it allows them to see both above and below the water surface at the same time. I hope this helps to clarify the concept.