Distorted Converging Lens

You have a converging lens made from a certain plastic that focuses sunlight when the lens is 12 cm from the ground. The lens is curved identically on both sides. You leave it out in the sun so that it melts a bit and becomes distorted the radius of curvature becomes 3/4 of what it was before, on both sides of the lens. How far from the ground must the lens now be held to focus sunlight?

One of the formulas I'm provided is $$(n-1)(\frac{1}{r_1} - \frac{1}{r_2})=\frac{1}{f}$$

Since the lens is curved identically on both sides, I would assume that $r = r_1 = r_2$, but that doesn't seem to work if I plug it into the equation above. $$(n-1)(\frac{1}{r}-\frac{1}{r})=0 \ne \frac{1}{12\text{cm}}$$

• You need to familiarize yourself with the sign convention. $r_2<0$ – garyp Mar 19 '18 at 0:19
• Thank you so much. That was exactly my problem. If you post that as an answer, I'll mark it as the accepted answer. – Christopher Crutchfield Mar 19 '18 at 0:26

All of the standard formulas of paraxial geometric optics adhere to a sign convention. There is more than one sign convention in use in the field. There's no obvious way to choose the signs, so a convention is adopted which is maintained throughout. So you have to familiarize yourself with the convention that is being used. In this case, since the final answer can't be zero, it's clear that one part of the sign convention requires that $r_2<0$.