Two lenses `L_(1)` and `L_(2)` are used to make a telescope. The larger lens `L_(1)` is a convex lens with both surfaces having radius of curvature eq

Two lenses `L_(1)` and `L_(2)` are used to make a telescope. The larger lens `L_(1)` is a convex lens with both surfaces having radius of curvature equal to 0.5 m. The smaller lens `L_(2)` has two surfaces with radius of curvature 4 cm. Both the lenses are made of glass having refractive index 1.5. The two lenses are mounted in a tube with separation between them equal to 1 cm less than the sum of their focal length.
(a) Find the position of the image formed by such a telescope for an object at a distance of 100 m from the objective lens `L_(1)`.
(b) What is the size of the image if object is 1 m high? Do you think that lateral magnification is a useful way to characterize a telescope?
(c) Angular magnification is defined as ratio of angle subtended by the image at the eyepiece to the angle subtended by the distant object at an unaided eye. Find the angular magnification of the above mentioned telescope.