How can I find the focal length of a lens silvered at one face?

[jd12345]

Homework Statement

Its not a specific question but a general one to solve similar questions. I need to find focal length of a lens silvered at one face

Homework Equations

The Attempt at a Solution

I know a convex lens silvered at one face will behave as an effective concave lens. But i need to find the equations. I can do it by individually solving each case but need a faster one.
My book says that the effective power, P = P(L) + P(M) +P(L)...P(L) is power of lens P(M) is power of mirror. I don't know why this works?

For two lenses kept close i understand why P = P1 + P2 but don't how this works in lens-mirror case too.
Any Help?

 

[sk9]

Actually it does. Just do it logically. I think that powers add because of formula being 1/v -1/u , so when you add p2 the image of 1 is oblect for 2 so basically it cancels out .p1 +p2 is just using the lens formula ignorantly . Ensure that proper sing and conditions are followed.Hope that helps