Question

The diameter of the plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 10⁸ m/s, the focal length of the lens is

15 cm

20 cm

30 cm

10 cm

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Solution

30 cm

straight R squared space equals straight d squared space plus space left parenthesis straight R minus straight t right parenthesis squared straight R squared minus straight d squared space equals space straight R squared space open curly brackets 1 minus straight t over straight R close curly brackets squared 1 minus straight d squared over straight R squared space equals space 1 minus fraction numerator 2 straight t over denominator straight R end fraction straight R space equals space fraction numerator left parenthesis 3 right parenthesis squared over denominator 2 space straight x left parenthesis 0.3 right parenthesis end fraction space equals space 90 over 6 space equals space 15 space cm 1 over straight f space equals space left parenthesis straight mu minus 1 right parenthesis space open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses 1 over straight f space equals space open parentheses 3 over 2 minus 1 close parentheses open parentheses 1 over 15 close parentheses straight f equals space 30 space cm

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