In 1911 the The Equivalence Principle led Einstein to believe that light would be deflected in the presence of a gravitational field.

It wasn't until 1915, however, after he had successfully incorporated curved spacetime into a gravitational theory of relativity, that he was able to make an accurate prediction as to the magnitude of such a deflection.

Returning to the mathematics, we have seen in our previous article Geodesics in Schwarzschild spacetime that the Schwarzschild geodesic equations can be used to derive **null geodesic equations** that describe the path of a light ray in spacetime.

Ultimately, for this purpose, we would like to express r as a function of Φ

Let's define **u = 1/r**

Replacing this expression in our original geodesic equation leads to

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The deflection is symetric with respect to Φ = π/2, and replacing the light speed by its real value c (in the Schwarzschild expression above we assumed c=1), gives

##### Example of the light deflection near the Sun

Let's calculate the deflection near the Sun, taking the following values:

G = 6.67 x 10^{-11} SI

M = 2 x 10^{30} kg

R_{0} = 700 000 km

c = 3 x 10^{8} ms^{-1}

gives ΔΦ = 8.5 x 10^{-6} rad = 4.85 x 10^{-4 } degrees = 0.029 ' = **1.74''**

That's the value that Eddington confirmed in his famous Eddington experiment during total solar eclipse of 29 May 1919.