. The London, Edinburgh and Dublin philosophical magazine and journal of science . ntinued from p. 411.] § 5. On the Accuracy required in Optical Surfaces. EOUCAULT, in the memoir already referred to, was, I be-lieve, the first to show that the errors of optical surfacesshould not exceed a moderate fraction of the wave-length oflight. In the case of perpendicular reflection from mirrors, theresults of § 4 lead to the conclusion that no considerable area ofthe surface should deviate from truth by more than one eighthof the wave-length. For a glass surface refracting at nearlyperpendicular incid
. The London, Edinburgh and Dublin philosophical magazine and journal of science . ntinued from p. 411.] § 5. On the Accuracy required in Optical Surfaces. EOUCAULT, in the memoir already referred to, was, I be-lieve, the first to show that the errors of optical surfacesshould not exceed a moderate fraction of the wave-length oflight. In the case of perpendicular reflection from mirrors, theresults of § 4 lead to the conclusion that no considerable area ofthe surface should deviate from truth by more than one eighthof the wave-length. For a glass surface refracting at nearlyperpendicular incidence the admissible error is about fourtimes as great. It will be understood, of course, that theerrors of one surface in an optical train may compensate forthose of another, all that is necessary being that the resultanterror of retardation rise nowhere to importance. In the case of oblique reflection at an angle <£, the error ofretardation due to an elevation B D (fig. 7) is QQ-QS = BD sec <£ (1- cos SQQ) = BD sec $ (1 + cos 2) = 2 BD cos , Fig. from which it follows that an error of given magnitude in thefigure of a surface is less important in oblique than in perpen-dicular reflection. At first sight this result appears to be con-tradicted by experience ; for it is well known to practical opti-cians that it is more difficult to secure a satisfactory perform-ance when reflection is oblique. The discrepancy is explainedin great measure when we take into account the kind of errorto which surfaces are most liable. No important deviationfrom a symmetrical form is to be feared; but a surface intendedto be plane may easily assume a slight general convexity orconcavity. Now in direct reflection, a small curvature isreadily and almost completely compensated by a small motionof the eyepiece giving a change of focus; but the compensa-tion obtainable in this way is much less perfect when thereflection is oblique. In the first case the family of surfaces 478 Lord Rayleighs
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