So for same distance, ∝ mass. So smaller separation → smaller mass.

February 22, 2026

So for same distance, ∝ mass. So smaller separation → smaller mass.

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But 0.8 < 1.6 → so mass must be less — but lensing is weaker. So smaller separation makes sense — weaker lensing.
So the given separateion (0.8) corresponds to less mass? But the claim is scale with mass.
Resolution: the proportionality is approximate, but the problem says "∝ mass / distance".
Therefore, 0.8 < 1.6 → mass of distant cluster is 0.8 / 1.6 = 0.5 times that of nearby.
So ratio = 0.5
But the question asks: "what is the ratio of the lensing mass of the distant cluster to the nearby one?"

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