A thin converging lens of focal length 20 cm, is used to produce a virtual, magnified image of an object. If..

Question

If it magnifies the object by 4 times, how far is the object from the lens?

Answer 1

Let's use the relation: hi/ho = di/do which says the ratio of height of

the object to the image is the same as the ratio of their distances.

Then we know that if the image is 4 times the size of the object,

it is 4 times as far away from the lens.  Now we use the relationship:

1/do + 1/di = 1/f which says the sum of the reciprocals of the distance

of the object and image is equal to the reciprocal of the focal length.

We know that di = 4 times do from the first relationship

and f is given as 20 cm.

Then 1/do + 1/4do = 1/20

5/4do = 1/20

4do = 100 and so

do = 25

The object is 25 cm. from the lens (and the image is 1 m. away)