Question

A plane mirror is placed $24.5$ cm in front of a concave mirror of focal length $10$ cm. Find where an object can be placed between two mirrors so that the first image of both mirrors coincides.

Answer 1

$\upsilon =-\left[24.5+24.5-x\right]$

$=\left[49-x\right]$

$u=-x\left[objectdis\tan ce\right]$

$\frac{1}{-(49-x)}+\frac{1}{-x}=\frac{1}{-10}$

$\frac{49}{49x-x^2}=\frac{1}{10}$

$x^2-49x+450=0$

$\left(x-35\right)\left(x-14\right)=0$

$x=35,14cm$