[UPSC IFoS 2023] Geometrical Optics (Q126, 15M)

Consider a thick equiconvex lens of refractive index 1 \cdot 5 as shown in the figure. The magnitude of the radii of curvatures of the two surfaces is 5\text{ cm}. The thickness of the lens is 1\text{ cm} and the lens is placed in the air. Obtain the system matrix and determine the focal length and the position of unit planes :