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Question
The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will ______.
Options
act as a convex lens only for the objects that lie on its curved side.
act as a concave lens for the objects that lie on its curved side.
act as a convex lens irrespective of the side on which the object lies.
act as a concave lens irrespective of side on which the object lies.
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Solution
The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will act as a convex lens irrespective of the side on which the object lies.
Explanation:
If object lies on curved side then R1 = +20 cm and R2 = `oo`, μ1 = 1, μ2 = 1.5
`1/f = (mu_2 - mu_1) (1/R_1 - 1/R_2)`
`1/f = (1.5 - 1) (1/20 - 1/oo) = 0.5/20 = 5/200 = 1/40`
F = + 40 cm
If object lies on plane side R1 = `oo` and R2 = – 20 cm, μ1 = 1, μ2 = 1.5
`1/f = (mu_2 - mu_1) (1/R_1-1/R_2)`
`1/f = (1.5 - 1)(1/oo - (- 1/20)) = 0.5 xx (+ 1/20)`
`1/f = 5/200`
f = + 40 cm
So, lens will always act as a convex lens irrespective of the side on which objects lie.
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