Question

Show mathematically that a diverging lens will alway produce an upright image. [i.e. prove that hi is positive if f is negative]

I'm not even sure how to start this. Can someone please help me?

Answer 1

You get an upright (virtual) image if the magnification is a negative number. The magnification is the ratio of the image distance si to the object distance so. The lens equation says that

1/so + 1/si = 1/f

If f is negative and so is positive, si must be negative. Therefore si/so must be negative also.

Answer 2

okay, but I'm not sure how that explains it algebraicall, could you please elaborate?

Answer 3

If 1/f is negative (as it is for a diverging lens), both so and si cannot be positive. That is the best is can do with the algebra.

You are restricted to positive values so (the object distance) with the source in front of the lens.