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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, 5:28 PM
Answered by Expert
Answer:
 
As shown in figure,  Two plano concave lenses are kept side by side so that their curved surfaces facing each other
and in between place is filled with liquid of refractive index 5/2.
This arrangment is a combination of three lenses kept together, i.e., two plano concave lenses made of glass and a
liquid convex lens in between them.
Let us find out the focal length of each lens by lens makers formula :- begin mathsize 12px style 1 over f equals space open parentheses mu minus 1 close parentheses open parentheses 1 over R subscript 1 minus 1 over R subscript 2 close parentheses end style,
where f is focal length of lens, μ is refractive index of material of lens and Rs are radii of curvature.
 
focal length f1 of plano concave lens with radius of curvature 20 cm :- begin mathsize 12px style 1 over f subscript 1 space equals space open parentheses 1.5 space minus space 1 close parentheses open parentheses fraction numerator 1 over denominator negative 20 end fraction minus 1 over infinity close parentheses space space o r space f subscript 1 space equals space minus space 40 space c m end style
focal length f2 of plano concave lens with radius of curvature 30 cm :- begin mathsize 12px style 1 over f subscript 2 space equals space open parentheses 1.5 space minus space 1 close parentheses open parentheses fraction numerator 1 over denominator negative 30 end fraction minus 1 over infinity close parentheses space space o r space f subscript 2 space equals space minus space 60 space c m end style
focal length f3 of liquid convex lens with radii of curvature 30 cm and 20 cm :- begin mathsize 12px style 1 over f subscript 3 space equals space open parentheses 2.5 space minus space 1 close parentheses open parentheses 1 over 30 plus 1 over 20 close parentheses space space o r space f subscript 3 space equals space 8 space c m end style
focal length F of combination of all three lenses :- begin mathsize 12px style 1 over F space equals space 1 over f subscript 1 plus space fraction numerator begin display style 1 end style over denominator begin display style f subscript 2 end style end fraction plus space fraction numerator begin display style 1 end style over denominator begin display style f subscript 3 end style end fraction space equals space fraction numerator 1 over denominator negative 40 end fraction plus fraction numerator 1 over denominator negative 60 end fraction plus 1 over 8 space equals space 1 over 12 space space semicolon space space space H e n c e space F space equals space 12 space c m end style
Answered by Expert 20th October 2018, 6:22 AM
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