A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in the figure. If the power of the original lens is 4D, then the power of a part of the divided lens is:
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When a lens is divided symmetrically, the power of each part is halved. This is because the focal length increases as the area decreases, and power is inversely proportional to focal length.
When a biconvex lens is divided symmetrically, the power of each part is proportional to its area. Since the lens is cut into four equal parts, the area of each part is one-fourth of the original lens. The power of the lens is inversely proportional to its focal length, and thus, the power of each part is the same as the original lens, but the focal length is reduced.
Since the focal length of each part is doubled, the power of each part is half of the original power:
\[
P_{\text{part}} = \frac{P_{\text{original}}}{2} = \frac{4D}{2} = 2D.
\]
Thus, the power of each part is \( \boxed{2D} \).
