A plano-convex lens made of glass (n = 1 5) has a focal length 10.0 cm.

(i) Calculate the radius of curvature of its curved surface.

(ii) If an identical plano-convex lens is placed in contact with the first (plane surfaces facing each other), what will be the power of the combination (in dioptres) ?

(i)

Given n =1.5

f = 10 cm

Since the line is plano convex :

∴R₁ (radius of curvature of plane surface) = ∞

R₂ = ?

We know that,

$1 over straight f space equals space left parenthesis n minus 1 right parenthesis space open parentheses 1 over R subscript 1 space minus space 1 over R subscript 2 close parentheses 1 over 10 space equals space left parenthesis 1.5 space minus 1 right parenthesis space open parentheses 1 over infinity space minus space 1 over R subscript 2 close parentheses 1 over 10 space equals space 0.5 space open parentheses negative space 1 over R subscript 2 close parentheses R subscript 2 space equals space minus 0.5 space x space 10 R subscript 2 space equals space minus space 5 space c m$

ii) When an identical planoconvexx lens is placed in contact with the first one. Then focal length of combination is given by

$1 over straight f space equals space left parenthesis n minus 1 right parenthesis space open parentheses 1 over R subscript 1 space minus space 1 over R subscript 2 close parentheses We space have comma space straight R subscript 1 space equals space space 5 space cm straight R subscript 2 space equals space minus 5 space cm Therefore comma space 1 over straight f space equals space left parenthesis 1.5 minus 1 right parenthesis space open parentheses 1 over italic 5 space plus space 1 over italic 5 close parentheses 1 over straight f space equals space 0.5 space straight x space 2 over 5 straight i. straight e. comma space straight f space equals space 5 space cm space straight f space equals space 0.05 space straight m Power comma space straight P space equals space fraction numerator 1 over denominator 0.005 end fraction space equals space 100 over 5 space equals space 20 space straight D$

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