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. - Londonproperty

Understanding the Context

What Determines Apparent Separation in Gravitational Lensing?

Apparent separation refers to how widely two light sources (e.g., stars or galaxies) appear to be spaced when viewed through a lens. In gravitational lensing, massive objects bend light, distorting the apparent positions of background sources. Crucially, the bending angle of light depends on the lens mass — more massive lenses produce stronger gravitational lensing effects.

This stronger bending increases the angular displacement between source images, effectively making them appear farther apart than they truly are — what is known as apparent binary separation.

Key Insights

The Apparent Paradox: 0.8 Mass vs 1.6 Mass — Why Larger Mass Sees Larger Apparent Separation

The key point is: apparent separation increases with lens mass, not decreases. So if we compare two lenses — one with 0.8 solar masses and another with 1.6 solar masses — the more massive lens (1.6 M☉) bends light more significantly. Thus, the angular separation between image paths widens.

This means:

• Lens mass ↑ → Apparent binary separation ↑
  
• Low mass (0.8 M☉) → Smaller apparent spread
  
• High mass (1.6 M☉) → Larger apparent spread

Therefore, saying “0.8 > 1.6” is factually incorrect — 0.8 is less than 1.6 — and consistent with stronger light bending for the more massive lens.

Final Thoughts

Why Misunderstanding Happens

The confusion often stems from equating lens mass with angular separation as if they were directly proportional without context. However, while mass increases bending, apparent separation also depends on:

• Impact parameter: How close the light passes the lens
  
• Lens-to-source distance
  
• Source redshift and intrinsic separation
  
• Lens equation geometry

But fundamentally, theory and observation agree: more massive lenses produce greater apparent separations, regardless of their specific mass values — as long as the mass is larger than the reference.