Question

There is a hole in the middle of small thin circular convex lens of focal length f = 4 cm. Diameter of hole is half of the diameter of lens. There is a point light source l at 9 cm away from wall. Where should the lens be placed from source in order to get a single circular illuminated spot on the wall which also has a sharp edge? Assume that the light passing through the hole goes parallel to the principle axis.

• A. 2 cm
• B. 3 cm
• C. 4 cm
• D. 6 cm

Answer 1

Answer: (B), (D)

The correct options are
B 3 cm
D 6 cm


From the diagram,
$\tan \alpha =\frac{R}{2y}$ or
$\tan \alpha =\frac{R}{9-x+y}$
$\Rightarrow \frac{R}{2y}=\frac{R}{9-x+y}$
$\Rightarrow y=9-x$
For the lens,
$u=x$ and $v=9-x+y$
By the lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\Rightarrow \frac{1}{4}=\frac{1}{9-x+y}+\frac{1}{x}\Rightarrow \frac{1}{4}=\frac{1}{(9-x)\times 2}+\frac{1}{x}$

$x=3\text{or}6$