Question

An object 3 cm tall is placed 15 cm to the left of a diverging lens having a focal length f=-30 cm. What is the size of the resulting image?

Answer 1

The lens equation is

1/u + 1/v = 1/f

where u is the object distance and v is the image distance. Distances to real objects and images are positive and to virtual objects and images, negative. Focal length of convex lens is positive and that of a concave lens is negative.

1/15 + 1/v = - 1/30

1/v = - 1/30 - 1/15 = -0.1

v = - 10 cm

i.e. it is 10 cm in front of the lens and virtual.

magnification = - v/u = - (-10/ 15) = 1.6

The image is virtual, upright and magnified 1.6 times so the image is 3x1.6 = 1.875 cm