A symmetric double convex lens is divided into two equal halves by...

The power of a lens is given by the lens maker's formula:

$P = \dfrac{1}{f} = (\mu - 1) \left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)<br><br>When a symmetric double convex lens is cut into two equal halves by a plane containing the principal axis, the radii of curvature$R_1 and $R_2$ of the refracting surfaces for each half remain exactly the same as those of the original lens.

Since the radii of curvature and the refractive index of the material do not change, the focal length $f$ of each half remains the same as that of the original lens. The only change is that the aperture of the lens is halved, which reduces the intensity of the image but does not affect the focal length.

As the focal length is unchanged, the power of each divided part is equal to the power of the original lens.

Therefore, the power of each part remains $4 \text{ D}$.