Spherical fish bowl: optical power, focal length and magnification

[kpl]

Q. There is a fish in a spherical fish bowl of radius r filled with water. The fish is at a distance l from the surface of the tank. An observer in air views the fish at a distance d from the tank.

Please see the attachment for the image.

I am supposed to find the optical power and focus length of the water-air interface, the magnification power of the fish tank and an expression for the distance (L) between the obsever and optical image of the fish.

Here are the attempts I have made:

Optical power = (n1-n2)/(-r)

Focus Length = f'=n2/P = -n2r/(n1-n2)
I used f' because I think it is a virtual image?

Magnification Power = -(Image Distance/Object Distance) =-((L-d)/-r)

L=(-n1/r + n2/l)

Can anyone tell me if these are correct or if I am at least going along in the right direction?

 

[wendy_feifei]

Try the refraction at a single surface formula
n₁/s+n₂/s'=(n₁-n₂)/r

here, n₁=1.33 (water); N₂=1 (air)
and note the sign of s should be negative as the fish is not on the incident-light side of the surface.