Question

A point object is placed at a distance of 20 cm from a thin planoconvex lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at

• A. 60 cm to the left of the system
• B. 60 cm to the right of the system
• C. 12 cm to the left of the system
• D. 12 cm to the right of the system

Answer 1

Answer: (C)

Focal length for the lens is given by,
$f=\frac{R}{\mu -1}=15$
After silvering the plane surface of the lens it converts to the thin plano convex mirror. focal length is now change. $\therefore$ For mirror focal length $f^{\prime }$ is given by, $f^{\prime }=\frac{R}{2(\mu -1)}=7.5$
Thus, for the mirror eq is, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f^{\prime }}$
Where $u=$ distance of the object from the mirror $=-20$,
and $v=$ distance of the image from the mirror
Thus, substituting the values of $f^{\prime }=7.5$ and $u=-20$
$\frac{1}{v}+\frac{1}{-20}=\frac{1}{7.5}$
$\therefore v=-12cm$ minus sign indicates that it is to the left of the system.