question_answer

In the figure shown, a thick plano convex lens is silvered at both the surfaces. A point source of light 'S' is inside the lens. The radius of curvature of the spherical curved surface is (8/3) cm and the distance 'S' from the curved surface is 2 cm. If the images formed due to direct reflections from the plane and curved surface coincide, then find the thickness of the lens in cm.

A) 5

B) 7

C) 3

D) 8

Correct Answer: C

Solution :

[c]

For mirror \[\frac{1}{v}+\frac{1}{-2}=\frac{3}{-4}\]\[\Rightarrow \]\[v=-\,4\]. This is at \[{{I}_{1}}\].

Image \[{{I}_{2}}\] is formed by plane mirror which coincides with \[{{I}_{1}}\]

From the figure it is \[2x=2\]

\[\sqrt{\frac{h}{g}-\frac{{{P}_{0}}}{\rho {{g}^{2}}}}\] \[x=1\,cm\]

\[{{P}_{0}}\]    thickness \[=\,3\,cm\]