• Pixel-art sticker of Lensa, personifying Gravitational Lensing, with the caption “Mass Bends The View.”

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Lensa

Gravitational Lensing Physics

\[\theta = \frac{4GM}{c^2 b}\]
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Meet Lensa, who bends the view: mass bends the path of light passing near it, so a galaxy cluster can magnify and distort galaxies behind it. Light grazing the Sun is deflected by about 1.75 arcseconds. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Lensa, a mass so large she bends the light passing by her.

General relativity says mass curves spacetime, and light follows that curvature. A ray passing a mass M at closest distance b is deflected by an angle θ ≈ 4GM/(c²b) when the deflection is small. That is twice what a simple Newtonian argument predicts, so measuring it was a test of Einstein's theory.

For light grazing the edge of the Sun, the formula gives about 1.75 arcseconds. During the total solar eclipse of 29 May 1919, expeditions led by Arthur Eddington and Frank Dyson measured star positions near the darkened Sun and found shifts in line with Einstein's value.

Today gravitational lensing is a working tool. Galaxy clusters act as natural telescopes, magnifying and distorting galaxies behind them into arcs. Lensing maps reveal dark matter, and microlensing by single stars has been used to find exoplanets.

The simple formula is for weak fields far from the mass. Near black holes, or when the source, lens and observer line up, the full theory gives rings and multiple images.

Equations

\[\theta = \frac{4GM}{c^2 b}\]
Symbols
SymbolMeaningUnit
\(\theta\) deflection angle (weak field) \(\mathrm{rad}\)
\(G\) Newtonian constant of gravitation \(\mathrm{N·m²/kg²}\)
\(M\) mass of the lens \(\mathrm{kg}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(b\) impact parameter (closest approach of the ray) \(\mathrm{m}\)