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I've been reading optics (both the cartesian and real/virtual sign convention) and I have some queries:

1. I was trying to work out problems involving silvered lenses (spherical lens with one side silvered) and first I tried to reason to myself how the imaging would take place. This what I believe:

for a real object in front of a silvered lens encountering first its nonsilvered side, a ray of light leaving the object would first undergo refraction from the nonsilvered side, reflection from the silvered side and then refraction from the first refracting surface again. This amounts to two refractions and one reflection.

However, the solved problems book I use reasons this way: a silvered lens can be considered as a normal spherical lens (nonsilvered that is) plus a spherical mirror (the curvature of which is identical to the silvered side of the given lens) at zero distance from each other.

I personally feel that my reasoning is correct because taking first a lens instead of one refracting surface means that the ray will encounter refraction at the second surface,

__followed__by reflection from the mirror which should not happen as the distance between the virtual boundary of the refracting medium and the spherical surface which has been silvered is zero so the ray immediately suffers reflection on reaching the geometric boundary of the surface. Who is correct?

To find out, I compared my equations (3 in number) with the three equations given as part of the solution and the equations are certainly different. So who really is correct?

2. As I am frequently required to change my point of view to accomodate rays incident from the left and from the right and also several lenses, prisms and mirrors combined and am required to find image parameters, I opted to use the sign convention outlined in Resnick, Halliday and Crane (virtual side/real side sign convention) as it is much more convenient than the cartesian convention which becomes very tedious and unwieldy. Yet, I would be grateful to receive some general opinions about the choice of sign convention for complex problems.

Thanks and cheers

Vivek