Question

You place an object 20 cm from a lens and find an image on the opposite side 30 cm from the lens. You calculate a focal length of 12 cm. You then move the object 30 cm from the same lens and once again measure the image distance. All your measurements and calculations are correct. What should you find when you calculate this focal length? a) It increased. b) It decreased. c) It stayed the same. d) There is not enough information to determine this focal length.

Answer 1

Answer:

The correct option is 'c': It stays same.

Explanation:

The focal length of any lens is obtained by using lens maker's formula as follows

$\frac{1}{f}=(\frac{n_{2}}{n_{2}}-1)(\frac{1}{R_{1}}-\frac{1}{R_{2}})$

where

$n_{2}$ is the refractive index of the material of lens

$n_{1}$ is the refractive index of the medium surrounding the lens

$R_{1},R_{2}$ are the radii of the 2 surfaces of the lens.

As we see that in the formula the focal length of the lens only depends on the refractive indexes and the radius of the lens thus we conclude that the focal length of the lens is independent on the position of object or image.