#16) A 4.0-cm tall object is placed 54.0 cm from a diverging lens having a focal

Question

#16)

A 4.0-cm tall object is placed 54.0 cm from a diverging lens having a focal length of magnitude 27.0 cm. What are the nature and location of the image? The image is

real, 1.3 cm tall, and 18.0 cm from the lens on the same side of the object. real, 4.0 cm tall, and 20 cm from the lens on the side opposite the object. virtual, 4.0 cm tall, and 20 cm from the lens on the side opposite the object. virtual, 1.3 cm tall, and 18.0 cm from the lens on the same side of the object. virtual, 2.0 cm tall, and 10 cm from the lens on the side opposite the object.

Explanation / Answer

Focal length of a diverging lens = -27 cm

using the lens equation we have

1/v + 1/u = 1/f

1/v + 1/54 = -1/27

v = -18 cm

size of image /size of object = - distance of image / distance of object

4 / Ho = -54/ -18

Ho = 1.3 cm

so the object is 1.3 cm tall , and 18 cm from the lens on the same side of the object

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