Question

A slide projector has to project a 35 mm slide $(25\text{mm}\times 23\text{mm})$ on a $2\text{m}\times 2\text{m}$ screen at a distance of 10 m from the lens. What should be the focal length of the lens in the projector ?

Answer 1

Magnification,

$\left(m\right)=\frac{2\times {10}^3}{35}=\frac{v}{u}$

$\therefore u=\frac{35}{2\times {10}^3}$

$v=\frac{35}{2\times {10}^3}\times 10\times {10}^3$

= 175 mm

From Lens Formula

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

$\Rightarrow \frac{1}{10}+\frac{1}{0.175}=\frac{1}{f}$

$\Rightarrow \frac{10175}{1750}=\frac{1}{f}$

$\Rightarrow f=\frac{1750}{10175},\mu =17.2\text{cm}$