Elements of natural philosophy (Volume 2-3) . two, and by formula (35), for any com-bination taken three and three, and so on. In general, it may be inferred from the precedingtable, that convex lenses tend to collect the incident rays,while concave lenses, on the contrary, tend to scatterthem. To construct thefocus; § 47. Transposing, in Equation (33), —? to the firstmember, we get / / F. u Illustration; Interpretation. Fig. 31. K- which shows that the vergency after, diminished bythat before deviation, gives a constant vergency measuredby the power of the lens. Hence, to construct the focus,
Elements of natural philosophy (Volume 2-3) . two, and by formula (35), for any com-bination taken three and three, and so on. In general, it may be inferred from the precedingtable, that convex lenses tend to collect the incident rays,while concave lenses, on the contrary, tend to scatterthem. To construct thefocus; § 47. Transposing, in Equation (33), —? to the firstmember, we get / / F. u Illustration; Interpretation. Fig. 31. K- which shows that the vergency after, diminished bythat before deviation, gives a constant vergency measuredby the power of the lens. Hence, to construct the focus,draw the extreme rayFD, and from the pointZ>, the line D H, mak-ing with the incidentr&yFD, produced, theangle IID K, equal tothe power of the lens;D H will be the de-viated ray, and the point F\ where it meets the axis, will be the , in the triangle F D F, the angle D F 0, measured by —., diminished by D F F, measured by —-, is equal to HD K, measured by —-; which ithe geometric interpretation of the above is 48. Suppose the conjugate foci to be in motion, Conjugate focisupposed in motion; and denote any two consecutive values of / by x and a?, ELEMENTS OF OPTICS. 209 and the corresponding values of f by y and y\ then Notation andEquation (33), eqaations; 1 1 + ?> y Fu v / 777 I } 5 y Fu x subtracting the second from the first we find, 1111 Transformationsy yf x x and reductions; reducing to a common denominator, and writing for theproducts y y and x x\ the quantities /2 and/2, towhich they will be sensibly equal, the Equation becomes yr — y x — x tf2 = f2 and dividing by the interval of time £, during which Time t,the change from x to x! takes place, which is the same introduccd;as that from y to y\ we have yf — y 1 x — x 1 /a t f or, (41): Relation betweenconjugate focal n 2 -f 2 distances and velocities of f2 ~~ f2 in which V denotes the velocity of the radiant, and Vthat of its conjugate focus; and since the denomina-tors must al
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