Question

The distance between an object and its image formed by a diverging lens is 47.7 cm. The focal length of the lens is -237.3 cm. (a) Find the image distance. cm (b) Find the object distance. cm

Answer 1

1/f = 1/v - 1/u

f = focal length, v = image distance, u = object distance.

taking all f, u and v as positive then:

1/f = (u - v)/uv

using your info: u - v = 47.7, f = -237.3 in the above equation gives:

uv = 47.7 f = -11319.21

then using:

u - v = 47.7
=> (47.7 + v)v = 11319.21

v^2 + 47.70v - 11319.21 = 0

solve the quadratic:

v = 85.18 or -132.88

v =132.88 cm and u = -85.18 *on the same side of the lens*. Of course the image for a diverging lens is always *virtual*.

If a negative focal length is entered to agree with the illustration, then the image is a virtual image on the same side of the lens as the object and will give a negative image distance.