Visitors at a science museum are invited to sit in a chair to the right of a ful
ID: 1299594 • Letter: V
Question
Visitors at a science museum are invited to sit in a chair to the right of a full-length diverging lens (f1 = -3.30 m) and observe a friend sitting in a second chair, 1.80 m to the left of the lens. The visitor then presses a button and a converging lens (f2 = +4.50 m) rises from the floor to a position 2.10 m to the right of the diverging lens, allowing the visitor to view the friend through both lenses at once. Find (a) the magnification of the friend when viewed through the diverging lens only and (b) the overall magnification of the friend when viewed through both lenses. Be sure to include the algebraic sign (+ or -) with your answers.
Explanation / Answer
Note that
1/f = 1/do + 1/di
where
f = focal length = -3.2 m
do = object distance = 1.5 m
di = image distance
Thus, solving for di,
di = -1.021276596 m
Thus, the magnification, m = -di/do,
m = 0.68085 [ANSWER, PART A]
********************
This will be do = 3.3213 m from the second lens.
Thus,
Note that
1/f = 1/do + 1/di
where
f = focal length = 3.5 m
do = object distance = 3.3213 m
di = image distance
Thus, solving for di,
di = -65.05064354 m
Thus, the magnification, m = -di/do,
m = 19.58589815
Thus, mtot = 0.68085 * 19.5858
= 13.33 [ANSWER, PART B]
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