# Optics: solid glass sphere

1. Oct 12, 2009

### Melawrghk

1. The problem statement, all variables and given/known data
A narrow beam of parallel rays enters a solid glass sphere in a radial direction. At what point outside the sphere are these rays brought to a focus? The radius of the sphere is 4.00cm and its index of refraction is 1.80

2. Relevant equations
na/s+nb/s'=(nb-na)/R

3. The attempt at a solution

I decided to split the sphere into two concave lenses (I'm not even sure this is a good idea though).

Then for the first one, I used the formula above and the following values:
s=infinity, s'=?, R=4.00, nb=1.8, na=1.00 to get s' of 9.0cm. At this point, I'm wondering if this 9.0cm is from the surface of the sphere? I decided to go with this idea.
Then s=2*4.00cm-9.0cm=-1.0cm for the second refracting surface. nb will still be 1.8 and na is 1. Finding s' this way, I get 1.5.

The textbook says it should be 0.5... I've run out of ideas for this question. I don't think it should be hard, maybe I'm overthinking it. Any hints?