How Does Refraction Affect Perceived Fish Size Underwater?

[kenth]

From This picture, I think the fish will be smaller but the problem is how small will it be?
(Fish "L" is the image of fish "K")
Let $H$ be the depth of fish "K", $\theta$ be the angle of eyes to y-axis and $n$ is the index of refraction of water.

 

[kuruman]

Continue your line of reasoning. What about the picture shows that the fish will appear smaller? How does Snell's law fit into the picture? Hint: If you look at two identical meter sticks, and one appears smaller than the other, what conclusion do you draw and how do you justify drawing it?

Is this a homework problem?

 

[kenth]

I made this picture myself so I made the fish appeared smaller because the light ray are shorter (I think). Snell's law would be use to solve this question because it has refraction.

This question isn't homework. There is solved problem about the distance that image move relative to the fish but I'm also curious about the size of the image.

 

[A.T.]

I'm also curious about the size of the image.

You have drawn rays for a single point of the fish. You need at least two points, to account for its size.

 

[Vanadium 50]

The fish is the same size whether it's in air or water. The size it appears, however, is different.

 

[Integral]

A issue with your drawing is the angle of refraction of the 2 parallel rays from the eye should remain parallel in the water, Why do they have different angles of refraction.
My gut tells me that if the fish is parallel with the surface of the water its size will be unaffected as the light rays are traversing the same amount of water. If the fish is not parallel with the surface then it is a different game.

 

[kuruman]

I made this picture myself so I made the fish appeared smaller because the light ray are shorter (I think). Snell's law would be use to solve this question because it has refraction.

This question isn't homework. There is solved problem about the distance that image move relative to the fish but I'm also curious about the size of the image.

The flat surface of the water will refract the light rays emanating from the two ends of the object the same way and as predicted by Snell's law. You need a curved surface such as a lens to see a differential effect between the two ends.

You must be familiar with ray diagrams. An arrow placed in front of a converging lens at distance larger than the focal length appears diminished because the rays emanating from different points along its length refract at larger angles the farther they are from the optical axis. In this case, the angular separation between the ends will be smaller with the lens than without and you conclude that the arrow looks smaller. If, however, you place a thick sheet of glass with flat parallel faces between you and the object, then the object will appear the same size although slightly displaced relative to its original position.

You may wish to try this experiment at home. Put an object, say a shiny butter knife, at the bottom of a deep pot. Take a picture. Fill the pot with water and take another picture being super careful to ensure that your phone (or camera) does not change position or angle relative to the object. Compare the two pictures. I will be curious to see the pictures if you actually perform this experiment.

 

[sophiecentaur]

My gut tells me that if the fish is parallel with the surface of the water its size will be unaffected as the light rays are traversing the same amount of water. If the fish is not parallel with the surface then it is a different game.

Assume the fish is horizontal and facing away from you. The effect is most marked in that orientation.
The rays from the tail of the fish comes at you from a different angle than the rays from the head so Snell will affect the two sets of rays differently. Question is whether the effect is greater or less for the head and tail. It's not hard to draw a diagram and produce two images - one of head and one of tail (Using Snell) and the differences in angles will show magnification or reduction.
If you also do the experiment then you can confirm the theory.

 

[A.T.]

My gut tells me that if the fish is parallel with the surface of the water its size will be unaffected as the light rays are traversing the same amount of water.

The angular size of the fish can be affected. Which way the effect goes, depends on the horizontal distance to the fish.