Are Back & Front Focal Lengths Equal for Thick Lenses?

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SUMMARY

The discussion confirms that the back focal length (BVP) and front focal length (FVP) of a thick plano-convex lens are not equal. The equations governing these focal lengths demonstrate that the BVP is calculated as (F1 + F2 - (d/n)F1F2)(1 - (d/n)F1) and the FVP as (F1 + F2 - (d/n)F1F2)(1 - (d/n)F2). With F1 set to 0 and F2 as the focal length of the curved side, the calculations show a clear distinction between BVP and FVP, affirming that the lens's thickness (d) plays a critical role in this difference.

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Homework Statement


is the back focal length equal to the front focal length of a thick lens ie a thick plano convex lens?

i know it is not but do not know how to clarify it please help

Homework Equations





The Attempt at a Solution

 
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A planoconvex lens is shaped like a capital D. One side has 0 power, and the other side has a power (because it has a curvature). Assume the lens has a thickness of d and a refractive index of n.

The BVP is given by (F1+F2-(d/n)F1F2)(1-(d/n)F1)
The FVP is given by (F1+F2-(d/n)F1F2)(1-(d/n)F2)

Subbing in F1 = 0, F2 = F2, we can clearly see that BVP is not the same as FVP (unless d is 0 but we disregard this, because the lens has a definite thickness).
 

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