Unless the 1.6 arcsec is for a larger mass? But 0.8 < 1.6.

February 22, 2026

Unless the 1.6 arcsec is for a larger mass? But 0.8 < 1.6.

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But 0.8 is less than 1.6, so if distance is same, then mass must be less. But gravitational lensing creates larger arcs for more massive clusters.
Thus, likely the proportionality is reversed in intuition. But the problem states directly: "apparent separation ∝ mass / distance".
So with same distance, separation ∝ mass. But 0.8 < 1.6 → mass of distant cluster < nearby? Contradiction.
Perhaps misread: "apparent separation between gravitational lenses is 0.8 arcseconds" — smaller than 1.6.
But the problem says: "if the lensing effect scales with mass and inversely proportional to distance", and gives "apparent separation ∝ mass / distance".
So at same distance, separation ∝ mass. But 0.8 < 1.6 → mass_P / d = 0.8, mass_N / d = 1.6 → mass_P = 0.8, mass_N = 1.6 → mass_P = half → mass_P / mass_N = 0.5

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