A diverging lens with a focal length of -13 cm is placed 11 cm to the right of a

Question

A diverging lens with a focal length of -13 cm is placed 11 cm to the right of a converging lens with a focal length of 20 cm. An object is placed 33 cm to the left of the converging lens. Where will the final image be located? Express your answer using two significant figures. d = cm to the left of the diverging lens Where will the image be if the diverging lens is 49 cm from the converging lens? Express your answer using two significant figures. Find the image location relative to the diverging lens. d = cm to the right of the diverging lens

Explanation / Answer

We know from lens formula.

1/f = 1/i + 1/o

i = o x f/ (o - f)

since the object's position is given wrt to converging lens, lets solve for it first.

i1 = 33 x 20/(33 - 20) = 50.77 cm

i1 = 50.77 cm , to the right of converging lens

the distance between the lens is 11 cm, so the object for the diverging lens is 39.77 cm

i2 = -39.77 x -13/(-39.77 + 13) = -19.31 cm

Hence, i2 = -19.31 cm, to the left of diverging lens.

B)Now the o2' will become

o2' = 49 - 50.77 = -1.77 cm

i2' = -1.77 x -13/(-1.77 + 13) = 2.05 cm

Hence, i2' = 2.05 cm to the right of the diverging lens.

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