Question

A 2 cm long pin is placed perpendicular to the principal axis of a convex lens of focal length 15 cm at distance of 25 cm from the lens. Find the position of image and its size. [3 MARKS]

Answer 1

Lens formula: 1 Mark
Position and size of image: 1 Mark each

1. Here, u = - 25 cm, f = +15

Using the Len's formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ we get

2. $\frac{1}{v}-\frac{1}{-25}=\frac{1}{+15}$

$v=37.5cm$

The positive sign shows that the image is formed on the right -hand side of the lens.

3. Magnification is given by

$m=\frac{h^{{}^{\prime }}}{h}=\frac{v}{u}$

$\frac{h^{{}^{\prime }}}{h}=\frac{37.5}{-25}=-1.5$

$h^{{}^{\prime }}=-1.5\times h=-1.5\times 2cm=-3cm$

The image of the pin is 3 cm long. The negative sign shows that it is formed below the principal axis,i.e the image is inverted.