A glass double-convex lens is positive in air, becomes ineffective when the liquid has the same refractive index as glass, and acts like a diverging lens in a denser liquid. For the plotted power in this question, the index contrast changes linearly with the liquid refractive index.
2026 Paper 1 Q4 · lens power versus liquid index
Straight-line relation: P = 15 − 10nL · zero power at nL = 1.5
Observation stage
Liquid index1.00
Power from index contrast
The lens power is proportional to the difference between glass index and liquid index.
ExpressionP = (1.5 − nL)(10)
Current valueP = +5.00 D
Converging lenspositive power for nL < 1.5
Index matchedP = 0 at nL = 1.5
Diverging lensnegative power for nL > 1.5
Derivation path
01 / INDEX CONTRAST
Use the glass-liquid contrast
As the liquid index increases, the optical contrast between glass and surroundings decreases linearly.
nglass − nL = 1.5 − nL
02 / GEOMETRY
The symmetric double-convex lens gives 10 m⁻¹
For radii +20 cm and −20 cm, the curvature factor is 1/R₁ − 1/R₂ = 10 m⁻¹.
1/0.20 − (−1/0.20) = 10
03 / POWER
The plot is a straight decreasing line
Substitution gives P = 15 − 10nL. It starts at +5 D for nL = 1 and crosses zero at 1.5.
P = 15 − 10nL
Correct power-index relation
P(nL) = 15 − 10nL
Correct plot: straight decreasing line crossing zero at nL = 1.5