# Physical Optics PT. II. the Corpuscular Theory of Light; Discussed Mathematically Volume 2

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 edition. Excerpt: ...spherical surfaces of given curvatures. The thin film of air being formed between spherical surfaces of given radii, the thickness of the film at any given point is easily expressed. Let ACB (figure 26) be the thin film of air between the spherical surfaces of the lenses which are in contact at C, with the common normal OCO' passing through O and O', the centers of curvatures of the surfaces. The interference is that of the rays arising from a ray SA incident nearly perpendicularly, having the retardation mn in the reflected rays equal to jaq in the transmitted rays, and equal to twice AB the thickness of the plate of air. Now drawing AM, BN perpendicularly upon OCO', we have AB= CM+ CN. Let r = radius of the upper spherical surface, r = lower and R = MA or NB the radius of the interference ring round C. Since CM and CN are the versed sines of the arcs CA and CB respectively, we have rM AM i?. AT BN R2. mTm- nearly' and the retardation 8 of the interfering rays = 2. MN, or 8=WI+). If the retardation occurred in'a heam incident ohliquely, we should have it of another form, as shewn in the next article. Substituting the value of 8 in the formula for the intensity 7 in the reflected rings, we have 7= U + r + 2W cos 27t (; + p)y. or, since I = T, if 7' be the intensity of the reflected light at A, then 7= T J2 jl + cos 2tr ( + J)J T, and the bright rings occur where where n may be any integer; and with a bright center where n=0, m rikr.r-n =;--r which gives the radius R of the bright ring, when n and X are given. In the same way the radii of the black rings are determined from the expression and g = (an + DX.r.r' 2(r + r) Giving the series of values 1, 2, 3, &c, we have the radii of the bright rings...