Finding the thickness of a double convex lens

[chris_0101]

Homework Statement

A double convex lens has a diameter of 5 cm and zero thickness at its edges. A point object on an axis through the center of the lens produces a real image on the opposite side. Both object and image distances are 30 cm, measured from a plane bisecting the lens. The lens has a refractive index of 1.52. Using the equivalence of optical path lengths through the center and edge of the lens, determine the thickness of the lens at its center.

Distance of object from bisecting line (do) = Distance of image from bisecting line (di) = 30cm

Diameter of lens = 5cm

length of lens from center axis = 2.5cm

refractive index of lens (n2) = 1.52

assuming n1 is air = 1.00

Homework Equations

OPL = (n1)(do) + (n2)(di)

The Attempt at a Solution

OPL = 1(30cm) + 1.52(30)
OPL = 30 + 45.6
OPL = 75.6

This answer is completely wrong because the answer at the back of the book says its 4.00mm from the center of the lens. If that is wrong then I really don't understand how to complete this question and if anyone can point me into the right direction, that would be great

Thanks

 

[SJS]

OPL(edge)=OPL(center)

OPL=n*distance

Your attempt at a solution assumes the thickness of the lens is 30cm (the distance through the medium by the refractive index of the medium)

OPL (edge) = (Lo + Li)*1 (distance from object to lens edge plus distance from lens edge to image, through)

OPL (center) = (distance to lens from object + distance to image from lens)*1 + 1.52*thickness

Haven't quite figured it out yet past there.