Page:Eddington A. Space Time and Gravitation. 1920.djvu/125

VI] is delayed in the shallow water and waits for the other. In the same way when the light waves pass near the sun, the end nearest the sun has the smaller velocity and the wave-front slews round; thus the course of the waves is bent.

Light moves more slowly in a material medium than in vacuum, the velocity being inversely proportional to the refractive index of the medium. The phenomenon of refraction is in fact caused by a slewing of the wave-front in passing into a region of smaller velocity. We can thus imitate the gravitational effect on light precisely, if we imagine the space round the sun filled with a refracting medium which gives the appropriate velocity of light. To give the velocity $$1 - 2m/r$$, the refractive index must be $$1/(1 - 2m/r)$$, or, very approximately, $$1 + 2m/r$$. At the surface of the sun, $$r = 697,000$$ km., $$m = 1.47$$ km., hence the necessary refractive index is 1.00000424. At a height above the sun equal to the radius it is 1.00000212.

Any problem on the paths of rays near the sun can now be solved by the methods of geometrical optics applied to the equivalent refracting medium. It is not difficult to show that the total deflection of a ray of light passing at a distance $$r$$ from the centre of the sun is (in circular measure) whereas the deflection of the same ray calculated on the Newtonian theory would be For a ray grazing the surface of the sun the numerical value of this deflection is