how far is the object from the lens?

Question

a magnifying glas uses a converging lens with a focal length of 14.5 cm. it produces a virtual and upright image that is 3.1 times larger than the object, how far is the object from the lens?


what is the image distance?


dont i use the eqn 1/p+1/q=1/f?

i got the answer wrong what am i doing wrong?

explain in details..........

Answer 1

Yes 1/p+1/q=1/f (p is v. image distance, q is object distance). But the trick is that p is negative for a virtual image (see ref.). So magnification M = -p/q. Substituting, 1/f = 1/p+1/(-p/M) = 1/p-M/p = (1-M)/p
Then p = (1-M)*f = -30.45 and q = 30.45/3.1 = 9.8226.
Checking, 1/((1/-30.45)+(1/9.8226)) = 14.5.