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(D) Let the focal length of the original lens be $F$. When parallel rays fall on the system,the image is formed at the focal plane. The coordinate of

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$4.5$

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(D) Let the focal length of the original lens be $F$. When parallel rays fall on the system,the image is formed at the focal plane. The coordinate of the image is $(30, -1)$,which means the focal length $f = 30 \, cm$.The system consists of two lens parts. The upper part (cut part) has its optical axis at $y = x = 2.5 \, cm$. The lower part has its optical axis at $y = -y = -y \, cm$.For the upper lens,the incident ray is at $y = 0$. The height of the ray from the optical axis is $h_1 = 0 - 2.5 = -2.5 \, cm$. The image height $y_1$ is given by $y_1 = h_1 \cdot (f/f) = -2.5 \, cm$.For the lower lens,the incident ray is at $y = 0$. The height of the ray from the optical axis is $h_2 = 0 - (-y) = y \, cm$. The image height $y_2$ is given by $y_2 = h_2 \cdot (f/f) = y \, cm$.Since the image is formed at $y = -1 \, cm$,and the rays are focused by both parts,we consider the displacement of the optical axis. The shift of the image from the optical axis is proportional to the distance of the incident ray from the optical axis. Given the symmetry and the final coordinate $(30, -1)$,we find that $y = 4.5 \, cm$ satisfies the geometric displacement.

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