The element of area being 22rr 2 sin 04,, we have f:2 l 2x r2 si n 2 d ?=gam, r so that the energy emitted from T is represented by 87r3 (D, - D) 2 T2 (9) D2 x4' on such a scale that the energy of the primary wave is unity per unit of wave-front area.
We will now consider in detail the important case in which uniform plane waves are resolved at a surface coincident with a wave-front (OQ).
We imagine a wave-front divided o x Q into elementary rings or zones - often named after Huygens, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.
If, however, the primary wave be spherical, and of radius a at the wave-front of resolution, then we kno* that at a distance r further on the amplitude of the primary wave will be diminished in the ratio a:(r+a).
In like manner may be treated other cases, such as that of a primary wave-front of unequal principal curvatures.
The incident waves are thus plane, and are limited to a plane aperture coincident with a wave-front.
For the alteration of wave-length entails, at the two limits of a diffracted wave-front, a relative retardation equal to mndX.
Hence, if a be the width of the diffracted beam, and do the angle through which the wave-front is turned, ado = dX, or dispersion = /a ..
18), the nearest point on the wave-front, is wholly intercepted, and on the left the integration is to be taken from s = CA to s = co.
The utility of the curve depends upon the fact that the elements of arc represent, in amplitude and phase, the component vibrations due to the corresponding portions of the primary wave-front.
18) the centre of the curve 0 is to be considered to correspond to that point C of the primary wave-front which lies nearest to P. The operative part, or parts, of the curve are of course those which represent the unobstructed portions of the primary wave.
" Let E = o,7 7 = o, =f (bt - x) be the displacements corresponding to the incident light; let O l be any point in the plane P (of the wave-front), dS an element of that plane adjacent to 01; and consider the disturbance due to that portion only of the incident disturbance which passes continually across dS.
If a wave front is in a given position, as a 1 (fig.
Consequently a wave front such as b 1 tends to turn upwards, as shown in the successive positions b 2, 3 and 4.
The velocity of any part of a wave front relative to the ground will be the normal velocity of sound + the velocity of the wind at that point.
But if the wind is against the sound the velocity of a point of the wave front is the normal velocity-the wind velocity at the point, and so decreases as we rise.
Keyphrases wave front sensing, confocal microscopy, multiphoton microscopy.
The actual calculation follows a similar course to that by which Huygens's conception of the resolution of a wave into components corresponding to the various parts of the wave-front is usually verified (see Diffraction Of Light).
Now the effect upon P of each element of the plane is proportional to its area; but it depends also upon the distance from P, and possibly upon the inclination of the secondary ray to the direction of vibration and to the wave-front.
2) in the recipient screen the vibration due to an element dS of the wave-front is (§ 2) - ?p s i nk(at-p), p being the distance between M and the element dS.
This therefore expresses the secondary disturbance at a distance r and in a direction making an angle cp with OZ (the direction of primary vibration) due to the element dS of the wave-front.
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