An elementary treatise on geometrical optics / by R. S. Heath.
- Heath, Robert Samuel.
- Date:
- 1897
Licence: Public Domain Mark
Credit: An elementary treatise on geometrical optics / by R. S. Heath. Source: Wellcome Collection.
Provider: This material has been provided by UCL Library Services. The original may be consulted at UCL (University College London)
36/254 page 20
![Let PO, OQ be the projections of AO, OB on any plane through the normal, P and Q being the projections of the points A, B respec- tively. Then the triangles APM, BQN are equal in all respects, by Euclid i. 26. Let t], 7)' be the acute angles which the incident and refracted rays make with the plane; 4>, <f>' the acute angles which the projections of these rays on the plane make with the normal. Then AP = n sin 7], BQ = pf sin tf, and therefore, since AP is equal to BQ, psmn = p sin rj'. This proves the first theorem. Also OP = p cos rj, OQ = /*'cos V; and therefore, since PM is equal to QN, p cos rj sin 4> = p cos if sin <\>, which proves the second theorem. 1Q In any refraction, the greater the angle of in- cidence, the greater will be the angle of deviation. For if 4>, f be the angles of incidence and refraction, sin 0 = p sin <£', sin <f> - sin </>' _ V> — 1. sln^Tsin-^7 P + 1' tani(^-f) = /^li.> tantt^f) /* + 1' and therefore that is, or finally, ton*<*-+0- £+1 * <++ ^](https://iiif.wellcomecollection.org/image/b21286036_0036.jp2/full/800%2C/0/default.jpg)
