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Home / Doubts and Solutions/NEET/Physics

Please answer the following question with explanation

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Asked by kkudgiri55 19th October 2018, 5:27 PM
Answered by Expert
Answer:
Let us use lens makers formula to get answer for this question: begin mathsize 12px style 1 over f equals left parenthesis mu minus 1 right parenthesis open parentheses 1 over R subscript 1 minus 1 over R subscript 2 close parentheses end style,
where f is focal length, μ is refractive index of material of lens, R1 is the radius of curvature of first surface
and R2 is radius of curvature of second surface.
 
we are given fA : fB = 2 : 1  or fB =2 fA ............................(1)
 
R1A  = (1/4) R2A   and   R1B = 2 R2B
 
where subscripts A and B stands for respective data of lens-A and lens-B
 
for lens-A : begin mathsize 12px style 1 over f subscript A space equals space left parenthesis mu minus 1 right parenthesis open parentheses 1 over R subscript 1 A end subscript plus fraction numerator 1 over denominator 4 R subscript 1 A end subscript end fraction close parentheses space equals space open parentheses mu minus 1 close parentheses 1 over R subscript 1 A end subscript 5 over 4 space...................... left parenthesis 2 right parenthesis end style
for lens-B, using eqn.(1) : begin mathsize 12px style 1 over f subscript B space equals 2 over f subscript A space equals space left parenthesis mu minus 1 right parenthesis open parentheses 1 over R subscript 1 B end subscript plus 2 over R subscript 1 B end subscript close parentheses space equals space open parentheses mu minus 1 close parentheses 3 over R subscript 1 B end subscript space...................... left parenthesis 3 right parenthesis end style
let us divide eqn.(1) by eqn.(2), we get begin mathsize 12px style 1 half space equals space R subscript 1 B end subscript over R subscript 1 A end subscript 5 over 12 space space space o r space R subscript 1 A end subscript space colon space R subscript 1 B space end subscript equals space 5 space colon space 6 end style
Answered by Expert 20th October 2018, 10:04 AM
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