Focal length of the lens?

Question

A 2.00-cm tall object is placed 40.0 cm from a lens. The resulting image is 8.00-cm tall and upright relative to the object. Determine the focal length of the lens.

Answer 1

To answer this quesiton, you need to first determine what type of lens you have.

Because the image is larger and upright, you have a converging (double convex) lens and you also know that the object has to be placed in front of the focal point for this to occur.  The image will be virtual on the same side as the object.

Using the magnification formula, you know that:

hi/ho=-di/do or di=-hi(do)/ho

di = -8(40)/2 = -160 cm

This means that the virtual image is actually 160 cm in front of the lens.

Now we can calculate the focal point of the lens using the formula:

1/f = 1/do + 1/di

1/f = 1/40 + 1/-160

1/f = 0.01875 or f = 53.3 cm

The focal length of the converging lens is 53.3 cm.