# Image of an Object Inside Hollow Glass Sphere

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1. Apr 17, 2016

### Kaan99

Hello,
This question is from 1990 Turkey National Physics Olympics. I tried my best to translate it clearly.

1. The problem statement, all variables and given/known data

https://s23.postimg.org/cotn29afv/Hollow+Spherical+Glass.jpg

The sphere of radius 2R has an empty sphere inside with radius R. In order for the image of an object on the inner surface of the sphere to be R/5 far away from the object (which is shown with an asterisk*) for an observer at the indicated position (göz), what should be the index of refraction of the glass? Where is the focal point of this optical system?

2. Relevant equations
Thin Lens Equation
Lensmaker's Equation

3. The attempt at a solution
The lens is made up of to circles of radii R and 2R, using lensmaker and thin lens eq.
$\frac{1}{f} = (n-1) (\frac{1}{R_1}-\frac{1}{R_2})=\frac{1}{d_o}+\frac{1}{d_i}$
$(n-1)(\frac{1}{-R}-\frac{1}{-2R})=\frac{1}{2R}+\frac{1}{d_i}$
$\frac{n-1}{-2R}=\frac{1}{2R}+\frac{1}{d_i}$
$d_i=\frac{n}{-2R}$

It turned out that my attempt wasn't accurate from the start, as it deviates from the solution provided. I couldn't understand how the first equation is formed in the solution.

The result is n=2 and f=4R.

2. Apr 19, 2016