Question

A concave mirror of focal length $20cm$ and a convex lens of focal length $10cm$ are kept with their optic axes parallel but separated by $0.5cm$ as shown in the figure. The distance between the lens and mirror is $10cm$ . An object of height $3mm$ is placed on the optic axis of lens at a distance $15cm$ from the lens. Find the length of the image formed by the mirror in $mm$ .

Answer 1

Answer: 3

For image formed by the lens
$\frac{1}{v_1}-\frac{1}{-15}=\frac{1}{+10}$
$\Rightarrow v_1=+30cm$
i.e. $20cm$ behind mirror
For mirror
$\frac{1}{v_2}+\frac{1}{20}=\frac{1}{-20}$
$\Rightarrow v_2=-10cm$
Overall magnification = $\left(\frac{30}{-15}\right)\times \left(\frac{10}{20}\right)=-1$
Length of image $=1\times 3=3mm$