A diverging lens with a focal length of -14 cm is placed10 cm to the right of a

Question

A diverging lens with a focal length of -14 cm is placed10 cm to the right of a converging lenswith a focal length of 18 cm. An object is placed 31 cm to the left of the converging lens. (a) Where will the final image be located?
1 cm left of the converging lens
(b) Where will the image be if the diverging lens is 34 cm from the converging lens?
2 cm right of the diverging lens (a) Where will the final image be located?
1 cm left of the converging lens
(b) Where will the image be if the diverging lens is 34 cm from the converging lens?
2 cm right of the diverging lens

Explanation / Answer

a) 1/f = 1/u +1/v

1/18 = 1/30 + 1/v

v = 45 cm

new object distance for diverging lens = 45-10 = 35 cm

1/f = 1/u + 1/v

1/-14 = 1/-35 + 1/v

v = -23.33 cm

so distance of image form converging lens = 23.333 - 10 = 13.33 cm (left)

b) if distance between mirrors = 37

new object distance for diverging lens = 45-37 = 8 cm

1/f = 1/u + 1/v

1/-14 = 1/-8 + 1/v

v = 18.667 cm

so final distance = 18.667 + 37 = 55.67 cm (right)

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