Physics lenses problems

Question

A converging lens has a focal length of 14 cm. The lens is used to produce an inverted image of a 3.0 mm long insect that appears to be 4.3 mm long.

What is the position of the insect (relative to the lens)

A lens has a point of divergence that is 84.0 cm from the center of the lens. 

What is the magnification of the image produced when the object is located 42.0 cm away from the lens?

Answer 1

1.

This will be a problem of two equations, two unknowns:

a = object position; b = image position

The lens equation: 1/a + 1/b = 1/f = 1/14

The magnification equation: m = - b/a = -4.3/3 (negative because the image is inverted).

Solve the two equations for a.

2.

a = 42cm, we need to find b = ?

The lens equation:

1/a + 1/b = 1/f

1/42 + 1/b = -1/84cm (f is negative for a divergent lens).

Solve that equation for b.

Magnification m = - b/a = ... (if the magnification ends up negative, the image is inverted).