Question

An object placed 91 cm in front of a converging lens forms an image 22 cm behind the lens. What is the focal length of the lens?

Answer 1

ANSWER

29.01 cm

EXPLANATION

Given:

• The distance from the object to a converging (convex) lens, do = -91 cm

,

• The distance from the image to the lens, di = 22 cm

Find:

• The focal length of the lens, f

The image is behind the lens, so its distance to the lens is positive while the distance from the object to the lens is negative. Using the lens equation,

$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$

We can find the focal length,

$f=\frac{1}{\frac{1}{d_o}+\frac{1}{d_i}}=\frac{1}{\frac{1}{-91cm}+\frac{1}{22cm}}\approx29.01cm$

Hence, the focal length of the lens is 29.01 cm.