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)

12 cm to the left of the system

Answer 2

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 $u =-20$
$\frac{1}{ v }+\frac{1}{-20}=\frac{1}{7.5}$
$\therefore v =-12 cm$ minus sign indicates that it is to the left of the system.