Cat & Fishbowl Refraction Problem

[bcjochim07]

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?

 

[bcjochim07]

no... actually nevermind... the fish sees the cat's face outside the bowl 36.14 cm

 

[baba89]

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.