Question

The flat face of a plano-convex lens of focal length $10 \,cm$ is silvered. $A$ point source placed $30\, cm$ in front of the curved surface will produce a

• A. real image 15 cm away from the lens
• B. real image 6 cm away from the lens
• C. virtual image 15 cm away from the lens
• D. virtual image 6 cm away from the lens

Answer 1

Answer: (B)

When a lens is silvered, it acts like a mirror with focal length $f.$
It is givem by $-\frac{1}{f}=\frac{2}{f_{l}}+\frac{1}{f_{m}}$
where,$f_l$ = focal length of lens and $f_m$ = focal length of mirror

$\Rightarrow -\frac{1}{f}=\frac{2}{10}+\frac{1}{\infty} $
$\Rightarrow f=-5\, cm $
Here, note that negative sign appears in formula because mirror obtained is concave in nature.
Here, $u = - 30 \,cm$
So, by mirror formula, we have
$\Rightarrow \frac{1}{f}= \frac{1}{\upsilon}+\frac{1}{u}$
$\Rightarrow \frac{1}{-5}=\frac{1}{\upsilon}+\frac{1}{-30}$
$\Rightarrow \frac{1}{\upsilon}=\frac{1}{-5}+\frac{1}{30}=\frac{16+1}{30}$
$\Rightarrow \upsilon=- 6 \,cm$
So, image is real and $6 \,cm$ in front.