Focal-length mirrors

At its simplest, the mirror is a circular disc, of diameter 2a and mean thickness f, simply supported at its periphery (Fig. 7.2). When horizontal, it will deflect under its own weight M when vertical it will not deflect significantly. We want this distortion (which changes the focal length and introduces aberrations into the mirror) to be small... 

For any two-mirror system we can use geometric optics to derive equations that describe some important parameters. (For derivations see Schroeder, 2000). The effective system focal length can be determined in terms of the individual focal lengths and mirror separation ... 

Conversely the two focal lengths for primary and secondary can be determined given a requirement on the mirror spacing, d and back focal length e by the following two equations. 

This interferometric dilatometer consists of a rather simple and small Michelson interferometer, in which the two arms are parallel, and of a 4He cryostat, in which the sample to be measured is hold. The sample is cooled to 4 K, and data are taken during the warm up of the cryostat. The optical path difference between the two arms depends on the sample length hence a variation of the sample length determines an interference signal. The Michelson interferometer consists of a He-Ne stabilized laser (A = 0.6328 xm), two cube corner prisms, a beam splitter, three mirrors and a silicon photodiode detector placed in the focal plane of a 25 mm focal length biconvex lens (see Fig. 13.1). 

As the beam leaves the prism predisperser, it is focused on the entrance slit of the grating monochromator. The slit is curved, has variable width, and opens symmetrically about the chief ray (optical center line of system). The monochromator itself is of the off-axis Littrow variety (James and Sternberg, 1969 Stewart, 1970 Jennings, 1974) and uses a double-pass system described by McCubbin (1961). The double-pass aspect of the system doubles the optical retardation of the incident wave front and theoretically doubles the resolution of the instrument. The principal collimating mirror is a 5-m-focal-length, 102-cm-diam parabola. 

The concentrating parabola has a focal length of 18 motel s, is 40 meters high and 54 meters wide, and the focal axis is 13 meters above the first floor. The parabola consists of 9,500 initially flat glass mirrors that were mechanically curved and adjusted to provide a solar image of minimum diameter at the focal point Almost two years were required to accomplish these two precise adjustments which were completed on I... 

Samples of 1 (200 mg) were sealed in evacuated Pyrex ampoules (inner diameter 4 mm) and immersed in a 500-mL Pyrex beaker filled with ice and water in such a way that no ice blocked the laser beam. The beam of an excimer laser (Lambda Physics, EMC 201 XeCl 17 ns pulses 50 Hz repetition rate 3 h X = 308 nm) was positioned vertically using two dielectric mirrors and focused to the desired intensity by a quartz-lens with a focal length of 20 cm. For low intensity irradiations, the ampoules were placed in front of a mercury arc at a distance of 5 cm. The product ratio depended on the light intensity. The compounds 1, 2, 3 and 4 were separated by gas chromatography or HPLC on RP18 and spectroscopically characterized after 93-97% conversion to 3 and 4. 

A mirror is placed past the focusing lens to reflect the beam vertically into the flame and parallel to the spectrometer slits. The fluorescence is collected by a 10 cm focal length lens and focused onto the entrance slit of a Spex 1800-11 spectrometer operated in second order. The spectral resolution is 0.1 nm. 

The same fixed optical system can be used for the spectral and topographic option, to provide the required dispersion on the OMA channels. The demagnification of 1/15 mentioned in a preceding section is obtained by a 381 lens (Fig. IB, S, 1C and IE, m) at its focal distance from the slit together with a Dallmeyer Ultrac camera lens, F/0.98 of focal length 25 mm (Fig. 1C, IE, p) in the beam of light diffracted from the grating or reflected from the mirror, 1/15. 

In the same way, the 13th harmonic beam at 61 nm was selected by a tin-foil filter and focused by a SiC concave mirror with a focal length of 50 mm. The angle of incidence was set at 7 degrees. Figure 9.9 shows the 1/e2 beam spot size of the 13th beam as a function of distance from the concave mirror. The... 

The F number of a grating monochromator is also determined by Eq. (2-1). In this case, / is the focal length of the collimator mirror, and D is usually calculated by... 

A spherical concave mirror of radius R — CP = CQ reflects an object at O (mirror-object distance OP = u) into image at / (mirror-image distance IP= v). If object moves to infinity (u = oo), then all rays from that object will converge at the principal focus point F f—FP = (1/2) CP—RI2] that is, the principal focal length f is half of the radius of curvature. 

The reciprocal of the focal length/(expressed in meters) is the diopter, which measures the "strength" of a mirror or lens. The images produced by mirrors or lenses can be constructed (Fig. 2.17). 

For mirrors, the equation is usually written 1/s + 1/s = 2/R = 1/f. A diverging mirror is convex to the incoming light, with negative f. From this fact we conclude that R is also negative. This form of the equation is consistent with that of the lens equation, and the interpretation of sign of focal length is the same also. But violence is done to the definition of R we used above, for refraction. 

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