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## Homework Statement

There is a problem in which we are supposed to calculate the focal length of a diverging lens by putting it in series with a converging lens of known focal length and measuring the resulting image.

Distances of objects all from a single common reference point:

Object: 100cm

Convex Lens: 55.9cm

Image from Convex Lens (this was found by removing diverging lens): 18.85

Diverging Lens: 31.5cm

Final Image: 6.5cm

Previously calculated focal length of converging lens has yielded answers between 19.7 and 20.4, so I will use 20.

## Homework Equations

1/f = 1/o + 1/i

My understanding is that f is negative if it's a diverging lens or mirror and the image distance is negative if it's a virtual image (meaning it's right side up).

## The Attempt at a Solution

This problem drives me nuts because everything I've heard in class and found on the internet says that you can calculate the final image in a multi-lens system by finding the image of the first lens and then using that as the object for the second lens, and also that the image of a diverging lens ALWAYS right side up and smaller. However this experimental data would indicate that the diverging lens magnified the image of the converging lens, which is supposed to be impossible.

Math: When you put the first image distance and object distance in terms of the converging lens and use the lens equation you get that the focal length of the lens is 20.13, which is consistent with my expectation. However when I do this with the diverging lens I get that the focal length is 25.6. I thought the focal length was supposed to be negative for diverging lenses? When I try to draw the ray diagram I have to do it like a converging lens to make it work. Should I conclude that we actually used 2 converging lenses rather than a diverging lens? That would be a very obnoxious result but I guess the guy who set it up could have switched the lenses. Please try this yourself to see if I'm doing it right.

Data in terms of converging lens:

Object: 44.1cm

Image 1: 37.05cm

Data in terms of converging lens:

Image 1: 12.65cm

Image 2: -25cm