Page:Elementary Text-book of Physics (Anthony, 1897).djvu/420

406 '''334. Law of Refraction.'''—If the incident wave pass from the one medium into the other, there is, in general, a change in the wave front, and a consequent change in the direction of the light. Let us first consider the simple case of a plane wave entering a homogeneous, isotropic medium of which the bounding surface is plane. Suppose both planes perpendicular to the plane of the paper, and let $$AB$$ (Fig. 99) represent the intersection of the surface of the medium, and $$mn$$ the intersection of the wave with that plane. Let $$v$$ represent the velocity of light in the medium above $$AB,$$ and $$v'$$ the velocity in the medium below it. Let $$m'o$$ be the position of the wave in the first medium after a time $$t.$$ Then $$mo$$ equals $$vt.$$ As the wave front passes from $$mn$$ to $$m'o,$$ the points of the separating surface between $$n$$ and $$o$$ are successively disturbed, and become centres of spherical waves propagated into the second medium with the velocity $$v'.$$ The wave surface of which the centre is $$n$$ would, at the end of time $$t,$$ have a radius $$nn = v't,$$ such that $$\frac{nn'}{nn} = \frac{v}{v'}\cdot$$ Similarly, the wave from any other point, as $$s,$$ would have a radius $$st'$$ such that $$\frac{st}{st'} = \frac{v}{v'},$$ and the wave surface within the second medium is evidently the plane $$on''.$$ As the direction of propagation is perpendicular to the wave front, $$op$$ will represent the direction of the light in the second medium. In the triangles $$non'$$ and $$non''$$ we have $$nn' = no \sin Aon',$$ and