Point-Mass Gravitational Lensing
Solve the point-lens equation to locate two images and the aligned Einstein ring.
Free theory articleSolve the point-lens equation to locate two images and the aligned Einstein ring.
Concept & interpretation
In astrophysics, a massive object can bend light from a background source. For a weak-field thin point-mass lens, the normalized lens equation is u = x - 1/x, where u is the source angular position and x is the image angular position, both normalized by the Einstein radius.
Native experiment
Open Point-Mass Gravitational Lensing to see how the images move relative to the source.
- Set Source separation u to 1 and Einstein radius arcsec to 1. Note the positive image at 1.618 arcsec, the negative image at -0.618 arcsec, and total magnification of ~1.34.
- Set Source separation u to 2. The images move to 2.414 arcsec and -0.414 arcsec, and magnification drops to ~1.06, closer to the unlensed case.
- Set Source separation u to 0. The two images merge into a full Einstein ring of radius 1 arcsec, representing an infinite point-source magnification limit.