An object 2.00 cm high is placed 38.9 cm to the left of a converging lens having

Question

An object 2.00 cm high is placed 38.9 cm to the left of a converging lens having a focal length of 33.9 cm. A diverging lens having a focal length of -20.0 cm is placed 110 cm to the right of the converging lens. (Use the correct sign conventions for the following answers.) (a) Determine the final position and magnification of the final image. (Give the final position as the image distance from the second lens.) final position cm magnification (b) Is the image upright or inverted? upright inverted (c) Repeat parts (a) and (b) for the case where the second lens is a converging lens having a focal length of +20.0 cm. image position cm magnification image orientation upright inverted

Explanation / Answer

Use the lens formula

1/f = 1/v + 1/u

1/33.9 = 1/v + 1/38.9

=> v = 263.742 cm

u' = 110 - 263.742 = - 153.742 cm

f' = - 20 cm

so, - 1/20 = 1/v' - 1/153.742

=> v' = - 23 cm [to the left of the diverging lens].

u'' = 110 - 23 = 87 cm

1/33.9 = 1/v'' + 1/87

=> v'' = 55.54 cm to the left of the converging lens.

m = m x m' x m'' = (v'' v' v) / (u'' u' u)

if m > 0, the image is upright else inverted.

c] Replace f = 33.9 cm by f = 20 cm and carry out the same calculation.

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