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Q. 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 $mm$ .
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NTA AbhyasNTA Abhyas 2022

Solution:

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 $=1\times 3=3mm$