Question

A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was 4D, the power of a cut-lens will be

• A. 2D
• B. 3D
• C. 4D
• D. 5D

Answer 1

The correct option is A

2D

Lets find the focal length of each cut lens in focus of focal length of the original lens
Now; $\frac{1}{f}=(x-1)\left(\frac{2}{R}\right)$ (Lets say x is the refractive index of the lens)
We get; $\frac{1}{R}=\frac{1}{2f(x-1)}$
Now; for one plano convex lens;
$\frac{1}{f^{\prime }}=(x-1)\left(\frac{1}{R}\right)$
$\Rightarrow \frac{1}{f^{\prime }}=(x-1)\left(\frac{1}{2f(x-1)}\right)$
$\Rightarrow f^{\prime }=2f$
Now, According to the problem;
$f=\frac{1}{4}\times 100=25cm$
$\therefore f^{\prime }=50cm$
$\therefore P^{\prime }=2D$