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find out the radius of curvature of a secondary mirror.

A Cassegrain astronomical telescope uses two mirrors to form the image. The larger (concave) objective mirror has a focal length f1 = +51.50 cm. A small convex secondary mirror is mounted d = 43.50 cm in front of the primary. As shown in figure, light is reflected from the secondary through a hole in the center of the primary, thus forming a real image 8.00 cm behind the primary mirror. What is the radius of curvature of the secondary mirror?

An aluminum rod 15 cm in length is heated from 10 degrees Celsius to 50 degrees Celcius.

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