another optics question

[jlmac2001]

I don't understand how to do the following problem. I don't even know where to start.

Problem: Show that, in the paraxial domain, the magnification produced by a single spherical interface between two continious media given by Mt=-n1s1/n2s0. Use the small-angle approximation for Snell's Law and approximate the angles by their tangents.

[mmwave]

Originally posted by jlmac2001
I don't understand how to do the following problem. I don't even know where to start.

Problem: Show that, in the paraxial domain, the magnification produced by a single spherical interface between two continious media given by Mt=-n1s1/n2s0. Use the small-angle approximation for Snell's Law and approximate the angles by their tangents.

This one seemed tough to me the first time too. It's way simpler than you think. There is only one surface so all you need is snell's law, draw two rays from your object, use geometry to get hi/ho and then replace the tangents with the angles det. from snell's law.

A good diagram helps. I got mine from Intro to Optics by Pedrotti.

A further hint is that you want to use sin alpha is approx. alpha in snell's law and then in the equation for hi/ho use tan alpha is approx. alpha. Does it help you to know the answer is correct?