Cat & Fishbowl Refraction Problem

  • Thread starter bcjochim07
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    Refraction
In summary, a goldfish living in a 50 cm diameter spherical fish bowl sees a cat's face as being 36.14 cm from the edge of the bowl, as a virtual image. However, this is only visible to an observer from outside the bowl.
  • #1
bcjochim07
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Homework Statement


A goldfish lives in a 50 cm diameter spherical fish bowl. The fish sees a cat watching it. If the cat's face is 20 cm from the edge of the bowl, how far from the edge does the fish seet it as being? (You can ignore the thin glass wall of the bowl).


Homework Equations





The Attempt at a Solution


(n1)/s + (n2)/s' = (n2-n1)/R

(1.0)/20cm + (1.33)/s' = (1.33-1.00)/(25cm)

s'= -36.14 cm The fish will see a virtual image of the cat's face inside the bowl 36.14 cm. Is this correct, or can only an observer from outside the bowl see this virtual image?
 
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  • #2
no... actually nevermind... the fish sees the cat's face outside the bowl 36.14 cm
 
  • #3




Yes, your calculation for the distance of the virtual image is correct. However, this is only applicable for an observer outside the bowl. The fish, being inside the bowl, would not be able to see the virtual image due to the refraction of light at the water-air interface. The fish would see the cat's face as if it is at a distance of 20 cm from the edge of the bowl, since light travels in a straight line in the medium of water and does not bend at the water-air interface for the fish. This phenomenon is known as total internal reflection and it is the reason why the fish cannot see the virtual image of the cat's face.
 

What is the "Cat & Fishbowl Refraction Problem"?

The Cat & Fishbowl Refraction Problem is a thought experiment that demonstrates the concept of refraction, which is the bending of light as it passes through different mediums. In this scenario, a cat is looking at a fish in a fishbowl filled with water. The fish appears to be in a different location due to the refraction of light through the curved surface of the water.

Why does the fish appear to be in a different location to the cat?

This is due to the refraction of light. As light passes from one medium (air) to another (water), it changes speed and direction. This bending of light causes the fish to appear to be in a different location to the cat.

What is the scientific explanation behind this phenomenon?

The scientific explanation for this phenomenon lies in Snell's Law, which states that the angle of refraction is dependent on the angle of incidence and the difference in the refractive indices of the two mediums. In this case, the refractive index of air is lower than that of water, causing the light to bend as it enters the fishbowl.

Does this phenomenon only occur with cats and fish in fishbowls?

No, this phenomenon can occur with any object that is viewed through a curved surface or different mediums. For example, a straw in a glass of water will also appear to be in a different location due to refraction.

How does this phenomenon impact our daily lives?

Refraction plays a crucial role in many aspects of our daily lives, such as in the design of glasses, magnifying glasses, and cameras. It also affects how we see objects underwater, and it is a fundamental principle in many branches of science, including optics, physics, and astronomy.

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