(a) Show that the lens equation can be written in the Newtonian form xx` = f2, where x is the distance of the object from the focal point on the front side of the lens, and x` is the distance of the image to the focal point on the other side of the lens. Calculate the location of an image if the object is placed 45.0cm in front of a convex lens with a focal length f of 32.0cm using.
(b) The standard form of the thin lens equation, and
(c) The Newtonian form, stated above.