Question

An illuminated object lies at a distance 1.0 m from a screen. A convex lens is used to form the image of the object on a screen placed at a distance of 75 cm from the lens. Find:

1. the focal length of the lens, and
2. the magnification.

Answer 1

Distance of object from screen = 1.0 m = 100 cm

v = 75 cm,

u = 100 – 75 = 25 cm = -25 cm

(i) f = ?

${\displaystyle \frac{1}{\text{f}}=\frac{1}{\text{v}}-\frac{1}{\text{u}}}$

= ${\displaystyle \frac{1}{75}-\left(\frac{1}{-25}\right)}$

= ${\displaystyle \frac{1}{75}+\frac{1}{25}}$

${\displaystyle \frac{1}{\text{f}}=\frac{1+3}{75}=\frac{4}{75}}$

f = ${\displaystyle \frac{75}{4}}$

f = 18.75

(ii) Magnification (m) = ${\displaystyle \frac{v}{u}=\frac{75}{-25}=-3}$

Magnification (m) = 3

The -ve symbol indicates that the created image is actual and inverted.