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A plane glass mirror of thickness $3 \mathrm{~cm}$ of material of $\mu=\frac{3}{2}$ is silvered on the black surface. When a point object is placed $9 \mathrm{~cm}$ from the front surface of the mirror, then the position of the brightest image from the front surface is
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Verified Answer
The correct answer is:
$1.3 \mathrm{~cm}$
A thick glass mirror produces a number of images. There is an apparent shift of actual silvered surface towards the unsilvered face.
Effective distance of the reflecting surface from
$$
\begin{aligned}
\text { unsilvered face } & =\frac{d}{\mu} \\
& =\frac{3}{3 / 2} \mathrm{~cm}=2 \mathrm{~cm}
\end{aligned}
$$
Distance of point object from effective reflecting surface $=9 \mathrm{~cm}+2 \mathrm{~cm}=11 \mathrm{~cm}$
Distance of image from point object.
$$
=11 \mathrm{~cm}+11 \mathrm{~cm}=22 \mathrm{~cm}
$$
Distance of image from unsilvered face
$$
=(22-9) \mathrm{cm}=13 \mathrm{~cm}
$$
Effective distance of the reflecting surface from
$$
\begin{aligned}
\text { unsilvered face } & =\frac{d}{\mu} \\
& =\frac{3}{3 / 2} \mathrm{~cm}=2 \mathrm{~cm}
\end{aligned}
$$
Distance of point object from effective reflecting surface $=9 \mathrm{~cm}+2 \mathrm{~cm}=11 \mathrm{~cm}$
Distance of image from point object.
$$
=11 \mathrm{~cm}+11 \mathrm{~cm}=22 \mathrm{~cm}
$$
Distance of image from unsilvered face
$$
=(22-9) \mathrm{cm}=13 \mathrm{~cm}
$$
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