Elements of natural philosophy (Volume 2-3) . rface. The difference of route of these portions willalso be 2 t, so that the effects should be the same oneither side of the lenses. Experiment shows, however,that this is not the case, for wherever there is totaldarkness by reflexion, there is a maximum of bright-ness by transmission. Hence, there must be half aninterval subtracted from the route at each internal re-1flexion / the cause of the loss being a change in densityand elasticity at the surfaces of contact of the glass andair. This will give for the interfering rays, in case ofreflected r
Elements of natural philosophy (Volume 2-3) . rface. The difference of route of these portions willalso be 2 t, so that the effects should be the same oneither side of the lenses. Experiment shows, however,that this is not the case, for wherever there is totaldarkness by reflexion, there is a maximum of bright-ness by transmission. Hence, there must be half aninterval subtracted from the route at each internal re-1flexion / the cause of the loss being a change in densityand elasticity at the surfaces of contact of the glass andair. This will give for the interfering rays, in case ofreflected rings, a difference of route expressed by accounted for: 2*+ ~ 2 Difference ofroute for reflectedrings; and for the transmitted, Fig. 75. 2 t + x. To ascertain the value of £, at thedifferent rings, call d, the diameter2 PII, of one of them, as determinedby actual measurement; r and / theradii of the surfaces, v and v\ the cor-responding versed sines of the arcs whose sines PII andPf H\ are equal to the semi-diameter of the ring in Same fortransmitted rings. To find r, at thedifferent rings; 288 NATURAL PHILOSOPHY. Equation fromthe figure; Then, for very small arcs, we have (4)* 2 r and Anotherequation; , (4) ^ = -—; 2r Value of t; whence < = „ _ v = { _ | Same for firstbright ring; In this way Newton found the thickness at the brightestpart of the first ring nearest the central black spot, to be0,00000561 of an inch. lie also found the diameters of Law of variation ,,, . , , ,-, ii» of diameters of the darkest rings to be as the square roots ot the evendark and bright numbers 0, 2 ,4:, 6 , &c, and those of the brightest asthe square roots of the odd numbers 1,3,5,7, & radii of the surfaces being great compared with thediameters of the rings, the value of I at the alternatepoints of greatest obscurity and illumination are as thenatural numbers rinjrs 6) Law of variationof t, at the darkand bright rings; Above resultscompared with X for yellow;
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