# Geometric optics

1. May 2, 2015

### whatisreality

1. The problem statement, all variables and given/known data
A fish 2cm long is floating in a spherical glass fishtank with radius 20cm. The glass is 0.8cm thick and has index of refraction n=1.56. The index of refraction of water is 1.33. Find the apparent position and length of the fish.

2. Relevant equations

3. The attempt at a solution
I tried just applying the same equations I would normally:
$\frac{n_a}{s} + \frac{n_b}{s'} = \frac{n_b-n_a}{R}$
s is object distance, s' image distance, R radius of curvature. I used s=10cm, s' unknown, R=-10cm and got s' to be -156/11.
The magnification at this point is
$m=-\frac{n_as'}{n_bs}$
So m= 1.209... and the fish appears to be 2.42cm long.
Problem is, if this is the right approach I don't really know how to interpret the answers. Is the observer at the interface between materials? Where does 0.8cm come into it? Can I just apply the same equations again to find what the person outside the fishtank sees?

2. May 2, 2015

### haruspex

I know it's more work, but it helps readers a lot if you post all your working. In the above, I can't tell what you are plugging in for the indices without trying to reproduce your answer.

3. May 3, 2015

### whatisreality

Well, I was only considering the first boundary between the water and the glass, so I used na=1.33 and nb=1.56.Then I don't know what to do about the second boundary between the glass and air.

4. May 3, 2015

### haruspex

Since the glass is only a shell, it would probably more accurate to ignore the glass and just consider air and water.
To bring the glass into it, draw a diagram. You have the fish on one side, a curved piece of glass, viewer on the other side. What are the radii of curvature of the inside and outside of the glass? Regard it as a lens.

5. May 4, 2015

### whatisreality

Does a lens of constant thickness behave according to the lensmakers equation? I think I can take the lens to be thin. We haven't actually covered lenses though...

6. May 4, 2015

### haruspex

Yes, I don't see why the glass would not behave approximately as a lens. You know the radii.
But I hadn't noticed you have treated the water as a flat surface. That will behave as a lens too. Puzzled that you'd be given this question before covering lenses in your studies.

7. May 5, 2015

### whatisreality

Oh. I didn't know that about the water. I think I'll wait until my professor goes through the answers! Thank you for helping :)