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**1. Homework Statement**

The lens and mirror in the figure below have focal lengths of +74.0 cm and -59.1 cm, respectively. An object is placed 1.00 m to the left of the lens as shown.

http://www.jmlproductions.net/jmlproductions/p36-54.gif [Broken]

I need to find the final image location.

**2. Homework Equations**

This problem uses the lens equation:

1/p + 1/q = 1/f

For verification, I use the equations M = -q/p and M

_{f}= M

_{1}M

_{2}as the second part asks for final magnification.

**3. The Attempt at a Solution**

I have tried this a few times. Calculate the image position for the first lens:

1/100 + 1/q = 1/74

1/((1/74)-(1/100)) = q

So q = 284.62 cm, so the distance of p for the mirror then is -q+100, which means that it's behind the mirror with p = -184.62 cm. Using the lens equation again:

1/-184.62 + 1/q = 1/-59.1

1/((1/-59.1)+(1/184.62)) = q

q = -86.93, so the image is formed in front of the mirror (? convex mirror? Should this happen?)

To convert q to p for the first lens again, add 100 and multiply by -1.

p = -13.07

Then find the final image position.

1/-13.07 + 1/q = 1/74

1/((1/74)+(1/13.7)) = q

q = 11.1

So add this to 100 to get final position at 111.1 cm

I have not actually submitted this answer, but using those numbers to calculate the final magnification, it is also incorrect as the magnification is wrong. What I do know is that the final image is inverted. Many thanks to those that help.

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