A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index n_L. The correct plot showing the variation of the power, in the units of diopter (D), as a function of n_L is:
A.
The focal length f of a lens immersed in a medium of refractive index n_L is given by the Lens Maker's formula: 1 f = ( n_g n_L - 1 ) ( 1 R_1 - 1 R_2 ) Given that the lens is double convex, the radii of curvature are R_1 = +20 cm = +0.2 m and R_2 = -20 cm = -0.2 m . The refractive index of the glass is n_g = 1.5. Substituting these values into the formula gives: 1 f = ( 1.5 n_L - 1 ) ( 1 0.2 - 1 -0.2 ) 1 f = ( 1.5 n_L - 1 ) (5 + 5) = 10 ( 1.5 n_L - 1 ) The power P of the lens is defined as the reciprocal of its focal length in meters: P = 1 f = 15 n_L - 10 This equation represents a hyperbola, indicating that the graph of P versus n_L is a curve, not a straight line. Evaluating the power at specific values of n_L yields P = 5 D at n_L = 1.0, P = 0 D at n_L = 1.5, and P = -2.5 D at n_L = 2.0. The second derivative d^2P dn_L^2 = 30 n_L^3 is positive for n_L > 0, meaning the curve is concave upwards. The correct plot shows a concave upwards curve passing through (1.0, 5), (1.5, 0), and (2.0, -2.5). Answer:
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