Question

An object is placed 4 cm in front of a convex lens of focal length 3 cm. Using the lens equation, find where the image will form and state whether it is a real or virtual image.

Answer 1

concave lenses are diverging lenses and have negative focal lengths
so we use the lens equation

1/i + 1/o = 1/f

here, the object distance = 4cm, f = - 3cm, so we have

1/i = - 1/3 - 1/4

i = -1.72 cm

the image forms 1.72 cm in front of the lens; it is a virtual image (the minus sign tells you the image is formed on the same side of the lens as the object)
from this problem, you can see that convex lenses always produce virutal images