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 6.80 cm to the right of the object. By placing a second lens at 26.75 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? converging diverging

(c) What is the total magnification?

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

Explanation / Answer

a) Let the object be at the origin

final V = 32 cm

Hence object distance for first lens is -6.8

using lens equaiton

v= uf/u+f = 3.7*6.8/ 3.1 = 8.11 cm

Hence the object for second lense is at 8.11 + 6.8 =15 cm from the origin

Second lense at 26.75

hence object distance u will be -11.75 cm and v = 5.25 cm

i/f = 1/5.25 + 1/ 11.75

f = 3.63 cm

nearly the same lense. which is converging as the focal length is positive.

Total maginification = v1v2/u1u2 = 8.11/6.8 * 5.25/11.75 = 0.53

Is the obejct was 12 cm the final image will be 6.4 cm

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