2) A converging lens (focal length fi) and a diverging lens (focal length
f2 < 0) are arranged so that the lenses are a distance d from one
another, as shown. If the distance d is set so that f1 + f2 < d < f1,
then the two lens system acts as a converging lens with an effective
focal length feff*. You can vary the focal length feff by varying the
separation d. (This tunable focal length feff is an important feature of
a zoom lens.) The two lenses shown have focal lengths f1 = 15.0 cm
and f2 = - -20.0 cm, but the distance d is unspecified.
*We can define the focal length of a compound lens as the image distance for incoming parallel lines (or
an object at infinity). So, feff for our two-lens system is measured from the center of the converging lens.
(a) Find the image distance s' 1 for the initially parallel rays that pass through the converging lens.
(b) Use your answer from part (a) to find S2 the object distance for the diverging lens.
(c) Use your answer from part (b) to find feff the effective focal length of the two-lens system.
Recall that feff is measured from the center of the converging lens.
(d) On the grid below, sketch a plot of feff vs. d. Clearly label your graph as appropriate.
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