In the last section of Einstein's paper of general relativity (1916), he deduced the curvature of light when passing massive objects. It says from Huygens' principle, the light rays must suffer a curvature of −∂γ/∂n at some point in the path (γ is the velocity). The Huygens' principle is about the propagation and interference of wave, how is it related with light rays' curvature?
Huygens' principle relates with the curvature of light because it describes how the wavefronts of light propagate and how they can be affected by external factors such as a gravitational field.
Huygens' principle states that every point on a wavefront can be considered as a source of secondary wavelets that spread out in all directions. The new wavefront at a later time is the envelope of these secondary wavelets. In the case of light, the wavefronts can be thought of as the path followed by individual photons.
A massive object has a non-zero energy density and pressure, and this energy density and pressure cause the fabric of space-time to warp or curve. This effect is known as "gravitational warping" or "gravitational lensing". According to general relativity, the presence of mass or energy causes space-time to be curved, and this curvature in turn affects the path of any object moving through it. When light passes by a massive object, its wavefronts curve which can be described mathematically by −∂γ/∂n. Einstein field equations relate the curvature of space-time to the energy and momentum of matter and radiation within it.
