Question

An object is 11.5 cm from a 3.20-diopter lens. How far from the lens is the image located?

I found the focal length using the refractive power given, and then used the thin lens equation to find d_i but I had no luck.

Answer 1

Here optical power = 3.20 diopter

So, focal length of the lens, f = 1/3.20 = 0.3125 m = 31.25 cm

Object distance u = 11.5 cm

image distance v = ?

use the thin lens formula -

1 / u + 1/ v = 1/f

put the values -

1 / 11.5 + 1 / v = 1 / 31.25

=> 1 / v = 1 / 31.25 - 1 / 11.25

=> 1 / v = - 0.0569

=> v = -17.58 cm

So, the image is located at a distance of 17.58 cm from the lens.

The negative sign shows that location of the image is towards the left of the lens, means in the same side as the object.