# The radii of the curvature of the spherical surfaces which is a lens

1. Jan 20, 2012

### komal bisht

the radii of the curvature of the spherical surfaces which is a lens of required focal length are not same. it forms image of an object. the surfaces of the lens facing the object and the image are interhanged. will the position of the image change?

2. Jan 20, 2012

### Simon Bridge

Re: optics

Welcome to PF.

This can be thought of as a composite lens like you find in the eyepiece of a telescope or microscope. What happens when you look through a telescope the wrong way?

What level is this aimed at?
Each bit of the lens can be represented by a 2x2 matrix depending on how the particular bit changes the angle and position of the light ray crossing it. The effect of the whole lens is the matrix multiplication of the matrixes.

In this case you have three elements (a curved surface, a gap through the glass and another curved surface) so the matrix for the lense would be the product of three: ABC
Turning the lens around changes the order of the matrixes to CBA
The question amounts to asking if ABC=CBA ... and, in general, that is "no".
The special case where this is equal means a special relationship between A and C which you remember are the spherical surfaces ... iirc: the radii of curvature have to be the same and and the sign of the curvatures have to be different (the lens must be bi-concave or bi-convex).

You don't have to understand how this works, so long as you know how to multiply 2x2 matrixes you can see that ABC is not CBA

Last edited: Jan 20, 2012
3. Mar 5, 2012

### komal bisht

Re: optics

Is r.m.s potential drop across the inductor zero at resonance in series LCR circuit?