Question

A converging lens has a focal length of magnitude 16.0 cm. Two objects A and B having equal height of 2.5 cm are placed in front of the lens at 13.0 cm and 19.0 cm, respectively. Find their image distances, heights, and describe each image (in terms of real, virtual, upright, inverted).

Answer 1

Given the focal length of the converging lens is 16cm. By sign convention the focal length f = 16cm. The height of the object is ho = 2.5cm.

(a) When the object is placed 13cm in front of the lens, by sign convention, the object distance is u = -13cm. If v is the image distance, then by lens formula,

So the image is formed 63.33cm from the lens. Since its value is negative, the image is formed on the same side of the object.

The magnification of the image is given by,

Since the magnification is positive, the image is virtual.

If hi is the height of the image, then

So the height of the image is 13.32cm. Since its value is positive, the image is upright.

(b) When the object is placed 19cm in front of the lens, by sign convention, the object distance is u = -19cm. If v is the image distance, then by lens formula,

So the image is formed 101.33cm from the lens. Since its value is positive, the image is formed on the opposite side of the object.

The magnification of the image is given by,

Since the magnification is negative, the image is real.

So the height of the image is 13.32cm. Since its value is negative, the image is inverted.