General and practical optics / by Lionel Laurance.

  • Laurance, Lionel.
Date:
1914
Catalogue details

Licence: In copyright

Credit: General and practical optics / by Lionel Laurance. Source: Wellcome Collection.

Provider: This material has been provided by UCL Library Services. The original may be consulted at UCL (University College London)

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    To find the value of cl we require two steps, thus (1) Find a from sin « = /x sin P/2; (2) then (l=2a - P. Expressed as a formula this becomes d=2 [sin-i (ix sin P/2)]-P that is, cl equals twice that angle whose sine is sin P/2 less P. Example.—AVhat is the angle of deviation of a prism whose principal angle is 60° and index 1*62 ? Here />i sin P/2 = 1-62 sin 30° = 1'62 x •5 = -81 and -81 = sin 54° (nearly) Therefore d = (2 x 54) - 60 = 48° To Calculate the Principal Angle.—The angle P at which a prism of known index must be ground, so that a certain angle of deviation be obtained is found as follows :— V + d\ . /P d sin ( ) sm ( + 2 sin _ sin P/2 cos <i/2 + cos P/2 sin dj'I _ ,, sin c?/2 — cos CL -r* , _ sin P/2 ' tan P/2 that is 7sin dl2 whence , -r,,^. sin dl2 tan P/2 = ^ IX - COS a/2 Example.—What angle must be given to a prism of 36° minimum devia- tion when /u, = 1 '586 1 P^ sin 18° ^ -3090 _ •3090_ .,gg.-^ ^^ 2 1-586-cos 18° 1-586-^9511 -6349 whence P/2 = 26° (nearly), and P = 52° Simplified Formulas.—When the angle of incidence or emergence is zero, i.e. when the incident ray is normal to the first surface, or the emergent ray is normal to the second, the formulae for finding d or P when the other two values are known, become simplified to _sin ((i + P) ^ sin P f?=[sin-i (/X sin P)]-P and , -r> sin cl