Elements of natural philosophy (Volume 2-3) . angle with each other, by meansof a little cement along their edges, and place theliquid between them where it will be held in sufficientquantity by capillary attraction. the formula. incident ray §26. When the ray is incident at right angles upon normal to first the firgt surface we ]iaye surface; 7 Consequences; 9 = 0, <p=o, and from Equations (10) and (11), there result, a = -vj/ a. whence Final result sin (a + S) = m sin a . . (13) Deviation at plane surfaces by refraction, will be againreferred to in a subsequent part of the text. ELEMENTS
Elements of natural philosophy (Volume 2-3) . angle with each other, by meansof a little cement along their edges, and place theliquid between them where it will be held in sufficientquantity by capillary attraction. the formula. incident ray §26. When the ray is incident at right angles upon normal to first the firgt surface we ]iaye surface; 7 Consequences; 9 = 0, <p=o, and from Equations (10) and (11), there result, a = -vj/ a. whence Final result sin (a + S) = m sin a . . (13) Deviation at plane surfaces by refraction, will be againreferred to in a subsequent part of the text. ELEMENTS OF OPTICS. 185 §27. Let MJST,MN\ be two planereflectors, meetingin a line projectedin M / S Dj a rayincident at thepoint D, and con-tained in a planeperpendicular tothe intersection jtfthe reflectors ; thisray will be devia-ted at the point 2),of the first reflec-tor, again at the point D\ of the second, and so on. Kequired the circumstances attending these deviations. Call the first angle of incidence <p Y second, <P2 third 9 3. Deviations of aray of light by reflectors, theplane ofincidence beingnormal to tkoirintersection; Notation; n th <Pn In the triangle P D D\ the angle at P is equal tothe inclination of the reflectors, which denote by i, andwre shall have <Pi — <P2 = h 92 - <P3 = h <P3 - <P4 = h <p„- a - Vn- , - <Pn = *; (14) Equations fromthe figure; and by addition, 9i -<P* n — 1 . i 9» = <Pi -»-l •.* Sum of thesoequations; (15) ISO NATURAL PHILOSOPHY. If 9 i be amultiple of i; If 9i be any multiple of i9 as n — 1 ; i9 ?! — ra — 1 . i = 0, (16) The ray will return upouitself. that is to say, the nth incidence will be perpendicular to the reflector, and the ray will, consequently, returnupon itself. Example 1st Suppose the angle made by the reflec- Example first; 4. 2. \ no i^ir* -1 » . tors to be 0 , and the nrst angle ot incidence, 01-9, = GO0;required the number of reflexions before the ray retracesits course. T
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