Question

In a Plano-convex lens the radius of curvature of the convex lens is $10\, cm$. If the plane side is polished, then the focal length will be (Refractive index $ \mu =1.5 $ ) :

• A. 15 cm
• B. 10 cm
• C. 2.5 cm
• D. 5 cm

Answer 1

Answer: (B)

If plane surface is silvered then there are two refraction and one reflection.
When light rays incident on Plano-convex lens surface polished, then the rays first refracted at convex surface, then reflected from polished plane surface and finally refracted from the convex surface.
Thus, there are two refractions and one reflection. Thus,
$\frac{1}{F}=\frac{2}{f_{l}}+\frac{1}{f_{m}}$
When plane surface is polished,
$f_{m}=\infty$
Also, $f_{l}=\frac{R}{u-1}$
Given, $R=10\, cm , $
$\mu=1.50$
$\therefore f_{l}=\frac{10}{(1.5-1)}$
$=\frac{10}{0.5}$
$=20 \,cm$
Hence, focal length of Plano-convex lens with plane surface polished will be
$\frac{1}{f}=\frac{2}{20}$
$\Rightarrow f=\frac{20}{2}$
$=10\, cm$