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

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To find the focal length of a lens silvered at one face, it is essential to understand that the lens behaves as an effective concave lens. The effective power of the system can be calculated using the formula P = P(L) + P(M) + P(L), where P(L) is the power of the lens and P(M) is the power of the mirror. This approach works because the powers of the lens and mirror add together due to the relationship defined by the lens formula, which considers the object and image distances. Proper signs and conditions must be adhered to when applying these formulas. Understanding this concept allows for a quicker solution to similar problems involving lens-mirror systems.
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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?
 
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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
 
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