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Home / Doubts and Solutions/NEET/Physics

Please answer the following question with explanation

qsnImg
Asked by kkudgiri55 20th October 2018, 3:37 PM
Answered by Expert
Answer:
We have lens maker formula for focal length f of the lens in terms of refractive index μ of material of lens
and radii of curvature R1 and R2
 
begin mathsize 12px style 1 over f equals open parentheses mu minus 1 close parentheses open parentheses 1 over R subscript 1 plus space 1 over R subscript 2 close parentheses space..................... left parenthesis 1 right parenthesis i f space mu space c h a n g e s space t o space mu plus d mu comma space t h e n space f o c a l space l e n g t h space f plus d f space b e c o m e s fraction numerator begin display style 1 end style over denominator begin display style f plus d f end style end fraction equals open parentheses mu plus d mu minus 1 close parentheses open parentheses fraction numerator begin display style 1 end style over denominator begin display style R subscript 1 end style end fraction plus space fraction numerator begin display style 1 end style over denominator begin display style R subscript 2 end style end fraction close parentheses space..................... left parenthesis 2 right parenthesis d i v i d i n g space e q n. left parenthesis 1 right parenthesis space b y space e a n. left parenthesis 2 right parenthesis comma space w e space g e t fraction numerator f plus d f over denominator f end fraction equals fraction numerator open parentheses mu minus 1 close parentheses over denominator open parentheses mu plus d mu minus 1 close parentheses end fraction space space space space o r space space space 1 plus fraction numerator d f over denominator f end fraction space equals space fraction numerator 1 over denominator 1 plus begin display style fraction numerator d mu over denominator mu end fraction end style begin display style fraction numerator mu over denominator mu minus 1 end fraction end style end fraction space............... left parenthesis 3 right parenthesis w e space a r e space g i v e n space t h a t comma space fraction numerator d mu over denominator mu end fraction equals 0.02 comma space a n d space w e space h a v e space fraction numerator mu over denominator mu minus 1 end fraction space equals fraction numerator 1.5 over denominator 0.5 end fraction equals 3 space comma space s u b s t i t u t i n g space t h e s e space v a l u e s space i n space e q n. left parenthesis 3 right parenthesis w e space g e t space comma space 1 plus fraction numerator d f over denominator f end fraction space equals space fraction numerator 1 over denominator 1 plus 0.02 cross times 3 end fraction space equals space 0.9433 comma space space o r space fraction numerator d f over denominator f end fraction space equals space minus 0.0567 space end style
 
Hence focal length decreases by 5.67%
Answered by Expert 21st October 2018, 2:17 AM
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