You would like to project an upright image at a position 32.0 cm to the right of

Question

You would like to project an upright image at a position 32.0 cm to the right of an object. You have a converging lens with focal length 3.70 cm located 5.60 cm to the right of the object. By placing a second lens at 28.00 cm to the right of the object, you obtain an image in the proper location.

(a) What is the focal length of the second lens?
cm

(b) Is this lens converging or diverging?

convergingdiverging    

(c) What is the total magnification?


(d) If the object is 12.0 cm high, what is the image height?
cm

Explanation / Answer

The key to this kind of problem is that the 1st (left) lens's
(intermediate) image is the 2nd (right) lens's object. Then using notation from
ref. 1 (+uN is object distance to left of lens N and +vN is image distance to
right of lens N), we have initially:
u1 = 0.056 m; f1 = 0.037 m; lens separation (sep) = 0.224 m; f2 = TBD; v2 = 0.04 m
Solving,
v1 = 1/(1/f1-1/u1) = 10.9 cm
u2 = sep - v1 = 11.5 cm
f2 = 1/(1/v2+1/u2) = 2.97 cm
Final Image location relative to lens 2 = v2 = 0.04 m
Final Image location relative to lens 1 = v2+sep = 0.264 m
Final Image location relative to object = v2+sep+u1 = 0.32 m
Magnification = v1v2/(u1u2) = 0.68
Image height = 0.68*0.12 = 0.0816 m

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