Question

A convex lens is cut in half along its principal axis and the two halves are separated by a distance of $12\text{cm}$. An object is placed $6\text{cm}$ in front of the lens as shown in Figure. Two sharp images are formed on the screen placed $80\text{cm}$ from the object. What is the focal length of the lens ?

• A. $12.50\text{cm}$
• B. $23.45\text{cm}$
• C. $17.30\text{cm}$
• D. $19.55\text{cm}$

Answer 1

The correct option is D $19.55\text{cm}$

Ray diagram : The path of a typical light ray is shown in the following figure. The element encountered is only a lens in either path of the light rays.

The lens is cut in half along the axis. So, both halves have the same focal length. Since two sharp images are formed on the screen, the result is equivalent to the lens displacement method with $D=80\text{cm}$ and $d=12\text{cm}$.
For the lens displacement method, the focal length of the lens is given by
$f=\frac{D^2-d^2}{4D}$ or $\frac{80\times 80-12\times 12}{4\times 80}$
$=\frac{6400-144}{320}=\frac{6256}{320}$
$f=19.55\text{cm}$