JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Geometrical Optics

A double convex lens has power

P

and same radii of curvature

R

of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is

(A)2 R
(B) $\frac{R}{2}$
(C) $\frac{3 R}{2}$
(D) $\frac{R}{3}$ ✓ Correct

Answer: (D)

Solution

For the double convex lens with both radii equal to

R

, the lensmaker's relation gives

P = (μ - 1) (\frac{1}{R} - \frac{1}{- R}) = \frac{2 ( μ - 1 )}{R}

. For a plano-convex lens of the same material and power

1.5 P

, only one curved face contributes:

1.5 P = \frac{( μ - 1 )}{R ^{'}}

. Dividing the second relation by the first,

1.5 = \frac{R}{2 R ^{'}}

, so

R^{'} = \frac{R}{3}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option

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