Question

A point object is placed at a distance of $20\, cm$ from a thin planoconvex lens of focal length $15 \,cm$, if the plane surface is silvered. The image will form at

• A. 60 cm left of A B
• B. 30 cm left of A B
• C. 12 cm left of A B
• D. 60 cm right of A B

Answer 1

Answer: (C)

For a silvered lens, the equivalent focal length is given by
$\frac{1}{f}=\frac{2}{f_{1}}+\frac{1}{f m}$
$\frac{1}{f}=\frac{2}{15}+\frac{1}{\infty} $
$\Rightarrow f =\frac{15}{2}$

A silvered lens acts as an equivalent concave mirror.
Applying mirror formula, we get
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}+\frac{1}{-20}=\frac{1}{\frac{-15}{2}}$
$\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{2}{15}=-\frac{5}{60}$
$\Rightarrow v =-12\, cm$ (to the left of $AB$)
(minus sign indicates that it is to the left of the system.)