A thin plano-convex lens acts like a concave mirror of focal length 0.2m when silvered from its plane surface.THe refractive index of the material of the lens is 1.5. What will be The radius of curvature of the convex surface of the lens??

Asked by Malavika Umesh | 26th Apr, 2015, 10:46: PM

Expert Answer:

begin mathsize 14px style Given colon space Focal space length comma space straight f subscript straight m space equals space 0.2 space straight m space Radius space of space curvature space of space curved space surface space left parenthesis straight R subscript 1 right parenthesis space equals space straight R space Radius space of space curvature space of space plane space side space left parenthesis straight R subscript 2 right parenthesis space equals space infinity Refractive space index space of space the space material space of space lens space left parenthesis straight mu right parenthesis space equals space 1.5 Since space straight a space thin space plano minus convex space lens space acts space like space straight a space concave space mirror space when space silvered space on space its space plane space surface comma space therefore comma space the space focal space length space of space lens space left parenthesis straight f right parenthesis space equals space 2 cross times space straight f subscript straight m space equals space 2 space cross times space 0.2 space equals space 0.4 space straight m. Using space len apostrophe straight s space maker space formula comma 1 over straight f equals left parenthesis straight mu minus 1 right parenthesis open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses fraction numerator 1 over denominator 0.4 end fraction equals left parenthesis 1.5 minus 1 right parenthesis open parentheses 1 over straight R equals 1 over infinity close parentheses fraction numerator 1 over denominator 0.4 end fraction equals 0.5 open parentheses 1 over straight R close parentheses straight R equals 0.5 space cross times space 0.4 space equals 0.2 space straight m space end style

Answered by Faiza Lambe | 27th Apr, 2015, 01:35: PM