PHYSICS HELP - optical images, magnification, etc.?

Question

PLEASE EXPLAIN BRIEFLY AND LABEL ANSWERS!

An object is located 3.5cm from the optical centre of a lens. The lens produces an image of magnification that is +0.667 the size of the object.

a) Is this lens a diverging or a converging lens? Explain your answer.

b) Find the position of the image and the focal length of the lens using the magnification equation and the thin lens equation.

Answer 1

(a) Since converging lenses always produce an inverted image and the lens in your problem produces an upright image, the lens must be diverging.

(b) the lens equation is

1 / f = 1 / do + 1 / di

f is the focal length of the lens
do is the object distance (3.5 cm)
di is the image distance (unknown)

but we also know that magnification m = - di / do = .667.

So use magnification to solve for the image distance, then the lens equation to find the focal length.