Photo-chemistry / by S.E. Sheppard.

  • Samuel Edward Sheppard
Date:
1914
Catalogue details

Licence: In copyright

Credit: Photo-chemistry / by S.E. Sheppard. Source: Wellcome Collection.

    28/484 page 12
    so that PO' = PO + NO', O'P — OP' — O'N', with sufficient approximation, i.e. so that the squares of differences are negligible. Then, with the same degree of approximation, NO' = OO' . cos POO'; O'N' = 00' . cos P'OO' In order to calculate cos POO', let the direction cosines of the lines PO and 00' be described with respect to a pair of rectangular axes, so that we have the directing lines OR, OS, and OK, where OK is supposed perpendicular to the plane of the paper, and must be supplied in imagination. Tall the angle of incidence PON, then the direction-cosines of PO are PO ; cos cfi, sin (f>, o and those of OO' 00' o, cos 0, sin 0 It is a theorem of analytical geometry that the cosine of any angle between two given lines is equal to the sum of the products of the corresponding direction-cosines of the same lines referred to an orthogonal pair of axes. Hence— cos POO' = sin $. cos B <'.os P'OO' = sin $', cos 0 supposing </>' to denote the angle of refraction. Hence, from the preceding equations— [x . PO' + \x. O'P' = [x . PO + [x . 00'. sin <f) cos 0 + fx . OP' — fx'. 00' sin if)'. cos 0 But we have from the definition of the refractive index the relation— fx . sin cf> — jx'. sin if)' hence, provided the point O be infinitely near to the point O', [X . PO + [x' . OP' = IX. PO' + [X' . O'P' exclusive of fractions of the second or higher order, which proves the theorem for a single refraction. The proof for a single reflection is relatively simpler.1 The vanishing of the 1 Sec P. Drude, Lehrb. d. Optik., p. io. S. Hirzel, Leipzig (1900).
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