$$ \\\\ \\text{The curved piece of glass used in a telescope is nothing but plano-convex lens,}\\\\ \\text{which when painted silver on its curved surface has a new focal length given by}\\\\ \\dfrac{1}{f'}=\\dfrac{2}{f}+\\dfrac{2}{R}\\\\ \\text{In this case, light travels twice through the lens and gets reflected once at the concave surface.}\\\\ \\text{From the question, we know that}\\\\ f'=12\\text{ cm}\\,\\text{and}\\,R=36\\text{ cm}\\\\ \\text{Clearly,}\\\\ \\dfrac{1}{12}=\\dfrac{2}{f}+\\dfrac{2}{36} \\\\ \\Rightarrow \\dfrac{2}{f}=\\dfrac{1}{12}-\\dfrac{2}{36} \\\\ \\Rightarrow \\dfrac{2}{f}=\\dfrac{1}{36} \\\\ \\therefore f=72\\text{ cm}$$","encodingFormat":"text/html"},"comment":{"@type":"Comment"}}]}]}