Positive parity
LIGHT LAB / EXPERIMENT 01
One universe.
More than one image.
Light from one distant source can reach Earth along different routes. Move the galaxies in its way and watch the images change, each carrying a different moment from the same source.
Move the galaxiesINTERACTIVE / TWO GALAXIES ALONG THE LINE OF SIGHT
Change the alignment.
Change what reaches Earth.
Drag a galaxy up or down in the path view, or use its sliders. The telescope view updates from the same lens model. Choose a red dwarf for an unresolved star, or a background galaxy to reveal stretched and mirrored structure.
The starting example and arrival times are shown below. Loading the interactive controls…
01 / THE JOURNEY
Between the source and Earth
THE LAST TRANSMISSION © 2026 DarkScienceDocs.com
02 / FROM EARTH
One source, several appearances
THE LAST TRANSMISSION © 2026 DarkScienceDocs.com
A / highlighted routeB / highlighted routeFaint lines / other image-center rays found
THE SAME EVENT / DIFFERENT ARRIVALS
Gravity changes the clock, too.
5 model image centers found. The two brightest routes differ by 10.29 days in this example.
A and B identify the two brightest image-center rays found, or representative ring rays at perfect alignment. Additional, often extremely faint, model images can appear. Labels are reassigned after changing an alignment.
Mirrored parity
The replay compresses the shared, very long flight. The displayed day labels are computed relative delays. A flash in the star, a separate supernova, or an illustrative compact event at the galaxy’s center, reaches the highlighted images at different observer times. Scrub the clock to compare them. Supernova mode uses a separate explosive source and an illustrative rise-and-fade curve; it does not turn the red dwarf into a supernova. Arrival labels track the same emission peak.
Inspect the image-center results
| Image | East (arcsec) | North (arcsec) | Relative arrival (days) | Signed magnification |
|---|---|---|---|---|
| 1 | 0.893 | 0.809 | 0.000 | 2.108 |
| 2 | -1.056 | -0.309 | 10.287 | -3.096 |
| 3 | 0.957 | -0.899 | 21.688 | -0.3370 |
| 4 | 0.948 | -0.663 | 27.832 | 0.003482 |
| 5 | -0.161 | 0.119 | 53.061 | 0.00004261 |
A finite numerical search can miss extremely faint or merging solutions near a caustic. “Found” is not a proof that every possible image has been recovered. Finite-source shapes are mapped separately, pixel by pixel, and do not depend on the image-center root count.
WHY THE IMAGES DISAGREE
A different route.
A different moment.
Earth sees the direction from which each ray arrives. Tracing that direction backward can lead to the same background source through more than one route. An extended galaxy can therefore appear in several places, stretched into arcs or with mirrored structure. The images do not have to look like simple rotated copies: the lens map can distort different parts by different amounts.
The travel-time difference has two contributions. A bent route changes the geometric distance, and the gravitational potential adds a time-delay contribution. The earliest route cannot be identified just by comparing the lengths of the lines in this drawing. The model calculates both terms before assigning relative arrival times.
When a source varies, astronomers can look for the same feature in several images at different times. That is the principle behind time-delay measurements in lensed quasars. Inferring the expansion rate of the Universe then also requires a defensible mass model and cosmological distances; this teaching example does not measure the Hubble constant.
STARS, ARCS & WHAT A TELESCOPE CAN SEE
Choose the source.
Read the distinction.
A red dwarf at these illustrative distances would normally be far too faint to detect, and its disk would remain unresolved. Star mode therefore shows image locations as softened points, with deliberately exaggerated visibility. It does not promise that a real instrument could observe this hypothetical star or resolve a stellar disk into a large arc.
Galaxy mode uses an extended, asymmetric spiral pattern. Every display pixel is traced backward through both galaxy masses to the same source pattern. The resulting arcs and flipped details come from the mapping, rather than separately painted or manually rotated duplicate galaxies. Surface brightness is mapped directly; lensing magnification increases apparent area, rather than making each surface element arbitrarily brighter.
Lensing is one of astronomy’s major probes of distant sources, mass distributions and cosmic structure. It works alongside spectroscopy, parallax, standard candles and many other kinds of evidence. A gravitational lens does not create another copy of a galaxy, and ordinary gravitational bending is not a prism that sorts these ray colors into different wavelengths.
THE MODEL / WHAT THESE NUMBERS MEAN
Follow the calculation.
Distances, masses, source size and animation
This is a static, weak-field, small-angle two-plane model in Euclidean space. The source is placed 1,500 Mpc away, approximately 4.89 billion light-years in that geometry. The lens planes are 480 and 990 Mpc from Earth. Their centers can move across the line of sight; the galaxies do not physically race across space as you drag them. Cosmological expansion, redshift factors, dust, microlensing by individual stars, detector noise and instrumental resolution are omitted.
Each mass is a circular, finite-mass cored profile, not a fitted map of a real galaxy. The compact core subtends 0.085 arcseconds at its lens plane. The source galaxy’s size and both source modes’ visibility are chosen for teaching. Star marker brightness is normalized and capped for legibility, so it is not a photometric prediction. Color marks identify paths; the source pattern keeps the same intrinsic colors across its images.
The flash and supernova replays are illustrative clock comparisons, not absolute travel-time animations. The Months / years preset uses more massive idealized lenses; its calculated delays are examples rather than forecasts for an observed event. A red dwarf is not a core-collapse supernova progenitor. Changing a galaxy stops the old replay and calculates a static configuration. Reduced-motion settings keep manual scrubbing available.
Lens equation, image parity and arrival time
For plane j, the transverse ray position is xj = Djθ − Σi<j(Dj − Di)α̂i. The cored deflection is α̂ = (4GM/c²)r/(r² + a²). A source image is a direction θ whose traced source-plane position matches the same source point.
The signed magnification of that point image is 1/det(∂β/∂θ). A negative sign means reversed parity, not negative light. The time calculation uses cT = Σ |xj+1 − xj|²/[2(Dj+1 − Dj)] − Σ ψ̂i, with ψ̂ = (2GM/c²) ln[(r² + a²)/rref²]. The common straight-ray term and arbitrary potential reference cancel from differences between images. Times are shown relative to the earliest image center found.
The schematic uses thin-plane bends. Real light follows a continuous trajectory through the gravitational field. Absolute delays and image configurations for an observed system require a more complete model and measurements.
CHECK THE RECORD
From the picture to the physics.
ESA/Webb: Gravitational lensing
An agency explanation of light deflection, magnification, multiple images and extended arcs. Use it to distinguish a real gravitational lens from the illustrative geometry here.
NASA/Hubble: One supernova, observed again
SN Refsdal appeared in multiple images in 2014; Hubble observed an additional predicted appearance in December 2015. It was the same explosion reaching Earth along a different route.
NASA: Star types and stellar endings
Low-mass red dwarfs and massive supernova progenitors have different stellar lives. The supernova replay switches to a separate explosive source, rather than making the example red dwarf collapse.
ESA/Hubble: Multiply imaged quasars
Real quasar systems illustrate repeated images and the use of source variability to measure arrival-time differences. These observations, rather than our replay, provide astronomical evidence.
Fleury, Larena & Uzan: Gravitational lenses in arbitrary space-times
The general multi-plane formalism derives lens maps, amplification and arrival times. The interactive model uses its static Euclidean specialization, not its full treatment of arbitrary backgrounds.
Schneider: Generalized multi-plane gravitational lensing
The lens equation and time-delay function are connected through Fermat’s principle. This is a mathematical foundation for why one must include both geometry and gravitational potential.
INVESTIGATION / AN UNEXPLAINED OPTICAL RECORD
A star blinked twice.
What changed the light?
Two closely resembling disturbances appeared in HD 89389’s light, 4.4 seconds apart. Could something in the foreground have altered the arriving light?
This event has not been identified as gravitational lensing. The lensing experiment demonstrates a separate, established mechanism; it does not explain or reproduce these optical pulses. The 4.4 seconds is the separation of the recorded disturbances, not a measured delay between lensed images.
OBSERVATION / A DELAYED SUPERNOVA
One explosion.
Several arrivals.
Supernova Athena offers an observational counterpart to the principle explored here: a foreground cluster can produce images of one explosion with different arrival times. The lab illustrates that mechanism without reproducing Athena’s cluster or calculating its forecast.