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A point object is placed at distance of $20 \mathrm{~cm}$ from a thin planoconvex lens of focal length $15 \mathrm{~cm}$. The plane surface of the lens is now silvered. The image created by the system is at
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$12 \mathrm{~cm}$ to the left of the system
$12 \mathrm{~cm}$ to the left of the system
Refraction from lens
$$
\begin{aligned}
\frac{1}{v_1}-\frac{1}{-20} & =\frac{1}{15} \\
v & =60 \mathrm{~cm}
\end{aligned}
$$
i.e., first image is formed at $60 \mathrm{~cm}$ to the right of lens system.
Reflection from mirror
After reflection from the mirror, the second image will be formed at a distance of $60 \mathrm{~cm}$ to the left of lens system.
Refraction from lens
$$
\begin{aligned}
\frac{1}{v_3}-\frac{1}{60} & =\frac{1}{15} \\
v_3 & =12 \mathrm{~cm}
\end{aligned}
$$
$$
\begin{aligned}
\frac{1}{v_1}-\frac{1}{-20} & =\frac{1}{15} \\
v & =60 \mathrm{~cm}
\end{aligned}
$$
i.e., first image is formed at $60 \mathrm{~cm}$ to the right of lens system.
Reflection from mirror
After reflection from the mirror, the second image will be formed at a distance of $60 \mathrm{~cm}$ to the left of lens system.
Refraction from lens
$$
\begin{aligned}
\frac{1}{v_3}-\frac{1}{60} & =\frac{1}{15} \\
v_3 & =12 \mathrm{~cm}
\end{aligned}
$$
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