An investigation has been made of the roots of a certain cubic equationudf(Yob) = 0, which arises in the theory of the type-111 triplet photographicudobjective. It has been shown that with the residuals and the parameterudvalues such as might be used in the type 111 triplet, this equation givesudthree positive roots of which only one leads to a practical solution.udIt was shown that if certain parameters which enter into the coefficientsudof Yob in this cubic equation are given values much greater than is usualudin a type 111 objective, a second root of the equation leads to a practicaludsolution. In this way, a new region of triplet solution has been opened - upudcharacterised by low powers for the components in the initial thin lensudarrangement. It was expected that this region would provide a basis for theuddevelopment of high aperture objectives.udThe general physical principles underlying the achievement of these highudvalues of initial parameters has involved a careful study of the propertiesudof thick meniscus shaped cemented triplet components of negative power.udA procedure for the design of a type 131 objective, which is the simplestudform of objective incorporating these principles, has been developed and isuddescribed with numerical examples. A study of more complex objectives isudneeded to exploit the principles which have been opened up in this work. Theudtime available for the investigation has not permitted the study of type 133udand other objectives from this point of view.
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