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have reached A’. However, the point A acts as the secondary center of radiation, and the rays travel backward from RS. Draw a circle with center A and radius AA’. By th<> time B reaches B’, A will have reached the circumference of the circle. A line drawn from B’ tangent to the circle contains two points of the new wave front. If we make a construction similar to that at A at any point, X, on the initial wave front, we can see that A’ B’ is the envelope of all the reflected waves, and is therefore the new wave front. Obviously AB and A’ B’ make equal angles with RS and satisfy the geometrical laws of reflection. For perpendicular incidence the light is reflected gack along its own path.
r > pure A.
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Let RS be a refracting surface, with the velocity of light in medium, I, V, in medium 2, V’. AB is a plane wave front approaching RS. Here again, if RS had not been there, after an interval of time T, A would have traveled a distance VT (equal to A A’ and BB’) and the wave front would have been at A’B’. However, the velocity of light in medium 2 is V’, and the distance traveled by the ray striking at A will be V’T. Construct a circle with A as center and radius V’T. This will represent the distance the wave from A has actually traveled in time T. Draw A”B’ tangent to the circle. Draw XZ the path, with re'fraction, of the ray from any point on AB. It will intersect RS at Y. Construct a circle with center Y, radius YZ times V’/V. It will be tangent to A”B’. Thus A”B’ is the
new wave front. AA’ and YD show the new direction of the refracted rays.
A water analogy is useful in discussing interference. Suppose that two stones are dropped into a pool of water so that they set up trains of waves that have the same wave length, amplitude, and velocity. They are represented in Figure 3. Solid lines are crests of waves ; dotted lines, troughs. Wherever the crest of the wave coming from A crosses the crest of a wave coming from B we have a wave with twice the amplitude of the original waves. The same is true of the troughs. These points of intensification come in straight lines ; as CD, EF, GH, etc. In between these lines we find other lines, MN, NP, QR, etc., where trough is superimposed on crest. Since they are of equal amplitude they cancel, and we see a line where there are no waves at all. As this happens to water waves we might expect it to happen to light as well. By ingenious devices scientists have accomplished this. The first was Young in 1807. He used a slit aperture and a screen pierced by
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