A diverging thin lens and a concave mirror have focal lengths of equal magnitude. An object is placed (3/2)f from the diverging lens and the mirror is placed a distance 3f on the other side of the lens. Using Gaussian optics, determine the final image of the system after two refractions. (Pedrotti-3, 2-22)
The Attempt at a Solution
I'm having trouble getting the final answer. After the first refraction, s' = -3f/5 so it is to the left of the lens. Then after the reflection, s' = 18f/13 so it is to the left of the mirror and to the right of the lens. So now in the last refraction, s = 3f - 18f/13 = 21f/13 but it should be negative since it is to the right of the lens. After using the formula (s = -21f/13, f = -f), I get s' =-21/8 so it is to the right of the lens but the answer should be: Final image between lens and mirror at 21f/34 from lens. If s = +21f/13 then it will work out. Why is it positive instead of negative even though the object is to the right of the lens before the second refraction?