Help me please. In the figure below, the converging lens? focal length is 13.5 c

Question

Help me please.

In the figure below, the converging lens? focal length is 13.5 cm, d = 11.7 cm, and the diverging lens? focal length is -14.5 cm. A 1.4 cm tall object is 7.8 cm to the left of the converging lens. (a) Where is the image formed by the converging lens, measured from that lens (using negative for a virtual image)? (b) How tall is the image formed by the converging lens (using negative for an inverted image)? (C) Where is the image formed by the diverging lens, measured from that lens (using negative for a virtual image)? (d) How tall is the image formed by the diverging lens (using negative for an inverted image)?

Explanation / Answer

Part A)

For the converging lens

1/f = 1/p + 1/q

1/13.5 = 1/7.8 + 1/q

q = -18.5 cm (18.5 cm to the left of the lens)

Part B)

h'/h = -q/p

h'/1.4 = -(-18.5)/(7.8)

h' = 3.32 cm

Part C)

Since the first image is 18.5 cm to the left of the converging lens, and the lenses are 11.7 cm wide, the image is 30.2 cm away from the lens, so...

1/-14.5 = 1/30.2 + 1/q

q = -9.80 cm (9.80 cm to the left of the diverging lens)

Part D)

h'/h = -q/p

h'/3.32 = -(-9.8)/(30.2)

h' = 1.08 cm

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