Reinterpret: The lensing effect size is proportional to mass and inversely proportional to square of distance? But problem states: "apparent separation ∝ mass / distance" — assuming monochromatic approximation.

February 22, 2026

Reinterpret: The lensing effect size is proportional to mass and inversely proportional to square of distance? But problem states: "apparent separation ∝ mass / distance" — assuming monochromatic approximation.

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/ 1.6 = 0.5 → mass ratio = 0.5
But lensing strength increases with mass, so distant cluster has half the lensing mass. But question asks for ratio of distant to nearby: 0.5 = 1/2
Wait — apparent separation is larger for more massive lens. So if 0.8 > 1.6? No — 0.8 < 1.6, so distant would appear smaller? Contradiction.
But 0.8 < 1.6, so if distance is same, mass ratio = 0.8 / 1.6 = 0.5. But that would imply less mass, contradicting stronger lensing.
Unless the formula is approximate and larger separation implies stronger lensing, so larger angular deflection corresponds to higher mass. But formula says separation ∝ mass / distance.
If distance is same, then separation ∝ mass. But observed separation is smaller (0.8 < 1.6), so mass must be smaller? That can’t be.

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