Question

A point object is placed at distance of 20cm from a thin plano convex lens of focal length 15cm.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

The correct option is C 12 cm to the left of the system

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.