Question

An object and it's real image are located at distance $25$ cm and $450$ cm respectively from the two principal loci, of a lens. Calculate the focal length of the lens.

Answer 1

$u=-\left(25\right)+f$

$v=\left(40+f\right)$

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

$\frac{1}{f+40}=\frac{1}{25+f}$ $=\frac{1}{f}$

$65f+2f=1000+65f+f^2$

$f^2=1000$

$=31.62cm.$

$u=25+31.62$

$=56.62cm.$

$v=40+31.62$

$=71.62cm$

$m=\frac{v}{u}$ $=\frac{71.62}{-56.62}$ $=-1.3$