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Figure 5.6. Fraunhofer diffraction of an incoming parallel beam by a single slit viewed from its short end. The slit is imagined to consist of the multiple segments shown. The image plane is taken to be at a very large (infinite) distance downward. (a) Forward direction (0 = 0) wherein the wavelets from all segments are in phase giving maximum intensity. (b) Direction 0 defined by sin 0 = X/d, in which the summed wavelets yield zero intensity, the first minimum of the response. (c) The one-dimensional response function, intensity vs. j(0). (d) The half angle of diffraction smearing 0min « X/d represents an uncertainty in the arrival direction that is equivalent to the wavefront arriving at the telescope aperture with one edge lagging the other by one wavelength.

Figure 5.6. Fraunhofer diffraction of an incoming parallel beam by a single slit viewed from its short end. The slit is imagined to consist of the multiple segments shown. The image plane is taken to be at a very large (infinite) distance downward. (a) Forward direction (0 = 0) wherein the wavelets from all segments are in phase giving maximum intensity. (b) Direction 0 defined by sin 0 = X/d, in which the summed wavelets yield zero intensity, the first minimum of the response. (c) The one-dimensional response function, intensity vs. j(0). (d) The half angle of diffraction smearing 0min « X/d represents an uncertainty in the arrival direction that is equivalent to the wavefront arriving at the telescope aperture with one edge lagging the other by one wavelength.

the aperture to bring the rays at each angle to a focus on a nearby focal plane. This simply moves the image plane closer and is the arrangement of a typical telescope.

In either of these cases (with and without a lens), for each angle 0, one can examine the interference of the wavelets from imaginary segments of the aperture. The simplest geometry to consider is an aperture which is a long, narrow slit (running into and out of the paper) of width d. Figures 6a,b show the narrow dimension of the slit. At the angle sin 0 = X/d (Fig. 6b), the rays from the left and center of the aperture are perfectly out of phase because the path length difference is exactly X/2. The rays from the segments just to the right of these (shown as short arrows in Fig. 6b) also are perfectly out of phase with each other for the same reason. In fact, each pair of segments in the left half of the slit has a partner in the right half which exactly cancels the first. Thus, one would expect no light at this particular angle,

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