## Focal Sentence Examples

- They are placed at a distance apart less than the
**focal**length of a, so that the wires of the micrometer, which must be distinctly seen, are beyond b. - The
**focal**length of the objective and the distance between the optical centre of the lens and the webs are so arranged that images of the divisions are formed in the plane of the webs, and the pitch of the screw is such that one division of the scale corresponds with some whole number of revolutions of the screw. - An important property is: the difference of the
**focal**distances of any point on the curve equals the transverse axis. - The tangent at any point bisects the angle between the
**focal**distances of the point, and the normal is equally inclined to the**focal**distances. - Two tangents from any point are equally inclined to the
**focal**distance of the point. **Focal**length was erected, and is still the principal instrument of its class at the observatory.- The harsher measures which about that time began to be adopted towards his co-religionists in France are usually assigned as the motive of this step. He now devoted himself during six years to the production of lenses of enormous
**focal**distance, which, mounted on high poles, and connected with the eye-piece by means of a cord, formed what were called "aerial telescopes." **Focal**length, are in the possession of the Royal Society.- The most important are: (I) To express the time of describing an elliptic arc under the Newtonian law of gravitation in terms of the
**focal**distances of the initial and final points, and the length of the chord joining them. - What is seen through the eye-piece in any case is the same as would be depicted upon a screen in the
**focal**plane. - By the principle of energy the illumination over the entire
**focal**plane must be equal to that over the diffracting area; and thus, in accordance with the suppositions by which (3) was obtained, its value when integrated from E= co to = -1-x, and from n = - oo to n = -1-oo should be equal to ab. - U 2 u It will be observed that, while the total intensity is proportional to ab, the intensity at the
**focal**point is proportional to a 2 b 2. - If the aperture be increased, not only is the total brightness over the
**focal**plane increased with it, but there is also a concentration of the diffraction pattern. - At the
**focal**point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture. - So long as there is no sensible discrepancy of phase there can be no sensible diminution of brightness as compared with that to be found at the
**focal**point itself. - Analytically expressed ff+ co x I 2 d dn=ff dxdy= A (9) We have seen that Io (the intensity at the
**focal**point) was equal to A 2 /X 2 f2. - In the case of the circular aperture the distribution of light is of course symmetrical with respect to the
**focal**point p=o, q=o; and C is a function of p and q only through 11 (p 2 -}-q 2). - Thus, if x = R cos 4), C =,r2R2J1(pR) pR and the illumination at distance r from the
**focal**point is 4T2 r 21rRr1 fX (2 fKr) a J The ascending series for J 1 (z), used by Sir G. - In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where r is the distance of any point in the
**focal**plane from the centre of the system. - Foucault, who employed a scale of equal bright and dark alternate parts; it was found to be proportional to the aperture and independent of the
**focal**length. - Thus in estimating the intensity at a
**focal**point, where, in the absence of aberration, all the secondary waves would have exactly the same phase, we see that an aberration nowhere exceeding 4X can have but little effect. - The function of a lens in forming an image is to compensate by its variable thickness the differences of phase which would otherwise exist between secondary waves arriving at the
**focal**point from various parts of the aperture. - If we suppose the diameter of the lens to be given (2R), and its
**focal**length f gradually to increase, the original differences of phase at the image of an infinitely distant luminous point diminish without limit. - Throughout the operation of increasing the
**focal**length, the resolving power of the instrument, which depends only upon the aperture, remains unchanged; and we thus arrive at the rather startling conclusion that a telescope of any degree of resolving power might be constructed without an object-glass, if only there were no limit to the admissible**focal**length. - The distance f i, which the actual
**focal**length must exceed, is given by d (f1 2 R2) x; so that f1 = 2 R2/X (1) Thus, if X = p j, R= i ?, we find f1= 800 inches. - As the minimum
**focal**length increases with the square of the aperture, a quite impracticable distance would be required to rival the resolving power of a modern telescope. - Calculation shows that, if the aperture be s in., an achromatic lens has no sensible advantage if the
**focal**length be greater than about II in. - If we suppose the
**focal**length to be 66 ft., a single lens is practically perfect up to an aperture of 1 . - A rotation of this amount should therefore be easily visible, but the limits of resolving power are being approached; and the conclusion is independent of the
**focal**length of the mirror, and of the employment of a telescope, provided of course that the reflected image is seen in focus, and that the full width of the mirror is utilized. - Curvature of the primary
**focal**line having a very injurious effect upon definition, it may be inferred from the excellent performance of these gratings that y is in fact small. - E is then the co-ordinate relatively to 0 of any
**focal**point 0' for which the retardation is R; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo. - If a retarding plate be now inserted so as to operate upon the pulses which come from one side of the grating, while leaving the remainder unaffected, we have to consider what happens at the
**focal**point chosen. - It is evident that the effect at the
**focal**point is the obliteration of the first and other spectra of odd order, so that as regards the spectrum of the first order we may consider that the two beams interfere. - - Employ the elliptic coordinates n,, and -=n+Vi, such that z=cch?, cchncos,y=cshnsin-; (1) then the curves for which n and are constant are confocal ellipses and hyperbolas, and -d(n,) =c 2 (ch 2 n - cost) = 2c 2 (ch2n-cos2) = r i r 2 = OD 2, (2) if OD is the semi-diameter conjugate to OP, and ri, r 2 the
**focal**distances, rl,r2 = c (ch n cos 0; r 2 = x2 +y2 = c 2 (ch 2 n - sin20 = 1c 2 (ch 2 7 7 +cos 2?). - Until recently these spherical lenses were numbered in terms of their
**focal**length, the inch being used as the unit. - Owing principally to differences in the length of the inch in various countries this method had great inconveniences, and now the unit is the refractive power of a lens whose
**focal**length is one metre. - A lens of twice its strength has a refractive power of 2 D, and a
**focal**length of half a metre, and so on. - The width of each of the portions aghc and acfe cut away from the lens was made slightly greater than the
**focal**length of lens X tangent of sun's greatest diameter. - It may be fixed at the end of a tube, of a suitable length to its
**focal**distance, as an object-glass, - the other end of the tube having an eye-glass fitted as usual in astronomical telescopes. **Focal**length, composed of a double concave flint lens and a double convex crown.**Focal**length.- On the other hand it is not necessary to reset the telescope after each reversal of the segments.4 When Bessel ordered the Konigsberg heliometer, he was anxious to have the segments made to move in cylindrical slides, of which the radius should be equal to the
**focal**length of the object-glass. - Struve also points out that by attaching a fine scale to the focusing slide of the eye-piece, and knowing the coefficient of expansion of the metal tube, the means would be provided for determining the absolute change of the
**focal**length of the object-glass at any time by the simple process of focusing on a double star. - Means of measuring the
**focal**point were provided; symmetrical motion was given to the slides; scales on each slide were provided instead of screws for measuring the separation of the segments, and both scales were read by the same micrometer microscope; a metallic thermometer was added to determine the temperature of the scales. **Focal**length) from the Repsolds, and the design for their construction was superintended by Struve, Auwers FIG.- Essentially the scale-value of the instrument depends on the relation of the
**focal**From Engineering, vol. - But the eye is tolerant of small changes in the
**focal**adjustment which sensibly affect the scale-value. - The amount of separation is very small, and depends on the thickness of the glass, the index of refraction and the
**focal**length of the telescope. - " the introduction of a diaphragm having two circular apertures touching each other in a point coinciding with the line of collimation of the telescope, and the diameter of each aperture exactly equal to the semidiameter of the cone of rays at the distance of the diaphragm from the
**focal**point of the object-glass." - The instrument has a
**focal**length of 54 ft.