the gravitational deflection of light

Light has no rest mass, so Newton would hardly expect gravity to grip it. Yet in curved spacetime a passing ray follows a geodesic, and near a massive body that geodesic bends. Starlight grazing the edge of the Sun is deflected by a small but measurable angle, so that stars seen near the Sun's limb during a total eclipse appear nudged slightly away from it. Confirming this was the 1919 expedition led by Arthur Eddington, the observation that made Einstein world-famous overnight.

For a ray passing a mass M with closest approach (impact parameter) b, general relativity predicts a deflection angle alpha = 4 G M / (c^2 b), which can also be written 2 r_s / b. At the limb of the Sun this comes to 1.75 arcseconds. The striking fact is that this is exactly twice the value a naive calculation gives by treating light as a Newtonian particle skimming past, which yields only 2 G M / (c^2 b). The extra factor of two is a clean, quantitative fingerprint of spacetime curvature.

The reason for the doubling is instructive and worth stating honestly. Half the deflection comes from the warping of time (the same effect behind gravitational redshift, and all that a Newtonian photon would feel), and the other, equal half comes from the curvature of space itself, which the Newtonian picture entirely omits. Today the same physics, scaled up, is a routine tool of astronomy: gravitational lensing by galaxies and clusters magnifies distant objects, splits quasars into multiple images, and weighs dark matter.