A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

A symmetric thin biconvex lens is cut into four equal parts by two mutually perpendicular planes passing through the principal axis.

Step 1: Understanding the Lens Division

• The original lens has power P = 4D.
• The lens is cut into four equal parts, meaning each part is a fraction of the whole lens.

Step 2: Effect of Cutting on Power

Case 1: Cut along the Principal Axis (Horizontally)

• If a convex lens is cut horizontally, the focal length of each part remains the same as the original lens.
• Since the power is given by $P=\frac{1}{f}$, cutting along this axis does not change the power.

Case 2: Cut along the Vertical Axis

• When the lens is cut vertically, on one side radius of curvature becomes infinite, making the focal length double.
• Cutting in this way makes the power half.

Thus, the power of each part becomes half of the original lens:

$\text{Power of each part}=2\mathrm{D}$