A parallel paraxial beam of light is incident on the arrangement as shown. $μ_{A} = 3/2, μ_{B} = 4/3$ , the two spherical surfaces are very close and each has a radius of curvature 10 cm. The distance of point where the rays are focussed from plane surface PQ is n cm. Then find the value of n.

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TestHub · Accepted Answer

For I st surface : v μ 2 ​ ​ − u μ 1 ​ ​ = R μ 2 ​ − μ 1 ​ ​ v 3/2 ​ − ∞ 1 ​ = + 10 3/2 − 1 ​ = 20 1 ​ v = 30 cm This will be the distance of object for second surface. For II nd surface : v ′ 4/3 ​ − + 30 3/2 ​ = − 10 4/3 − 3/2 ​ 3 v ′ 4 ​ − 20 1 ​ = 60 1 ​ v ′ = + 20 cm. For III rd surface : u = 20 − 16 = 4 & R = ∞ V 1 ​ − + 4 4/3 ​ = ∞ μ 2 ​ − μ 1 ​ ​ = 0 V ′′ = 3 cm

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