How Deep Does the Fish and Its Image Appear in a Pool?

[oddwolf]

Homework Statement

A 2 meter deep swimming pool is filled with water. A mirror is placed at the bottom and a small fish swims 5 cm (0.05m) below the surface. If you look at the swimming pool from above, how deep does the fish appear to be (a), and how deep does it's image appear to be (b)?

a1 = 0.05 m
a2 = 2.00 m
n_air = 1
n_water = 1.33

Homework Equations

n1/a1 + n2/a2 = (n2 - n1)/r

The Attempt at a Solution

Not so sure with (a), but without using the formula or anything on (b), my intuition tells me that the mirror-image should be 15+15+5 centimetres below the surface. Would really appreciate some help with (a) and some input.

Thanks in advance!

 

[ehild]

Is any spherical surface mentioned in the problem?

ehild

 

[oddwolf]

The only hint my book gave me is to use the formula for refraction in spherical surface.

 

[ehild]

Well, it was not a helpful hint then.
You certainly know that the apparent depth of an object in water (d') is shorter than the real depth d. How are d and d' related?
See:
http://www.schoolphysics.co.uk/age11-14/Light/text/Real_and_apparent_depth/index.html

ehild

 

[rktpro]

And you can derive hell lot of equations from what ehild provided you. :D