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A double convex lens immersed in a liquid: how its power in dioptres varies with the liquid's refractive index

A double convex glass lens (n = 1.5, R = 20 cm) sits in a tank whose liquid index n_L you change. Its rays converge, pass straight when the lens vanishes at n_L = 1.5, then diverge, while a plotter draws the power: 1/f is a curve (A), the optical power n_L/f a straight line (B) - the official key accepts A or B.

Sub-topics covered

• Refraction at a spherical surface: surface power (n2 - n1)/R
• Thin lens in a medium: optical power = sum of the surface powers = (n_g - n_L)(1/R1 - 1/R2)
• Lens-maker's formula in a medium: 1/f = (n_g/n_L - 1)(1/R1 - 1/R2)
• A lens vanishes when n_L = n_g and changes from converging to diverging when n_L > n_g
• Two definitions of power in a medium: 1/f (a hyperbola in n_L) and n_L/f (linear in n_L)

What it teaches

• Each surface of the lens bends light by (n_g - n_L)/R, so the bending depends on the index difference with the liquid
• Optical power n_L/f = 10(1.5 - n_L) D: a straight line through 5 D, 0 and -5 D at n_L = 1, 1.5, 2 - plot (B)
• 1/f = 10(1.5/n_L - 1) D: a curve (hyperbola, concave up) through 5 D, 0 and -2.5 D - plot (A)
• At n_L = 1.5 there is no refraction: f is infinite and the power is zero, so plots that diverge there (C, D) show f, not power
• The official key accepts A or B because the two plots are the two standard definitions of power in a medium

Simulation ID

• ADV-2026-P1-PHY-Q04 · revision 1

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