Journal of the Society of Motion Picture Engineers (1930-1949)

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658 ELLSWORTH D. COOK [j. s. M. P. E. distance, V, from the lens. The ordinates along ray, AM, will be called W while those along BP will be called W", then (9) If the original or primary aperture had a width of 2W, the image widths, 2Wi and 2W%, for the extreme indices of refraction are known. At the point of intersection of rays, BP and AM, it is seen that W' and W" are equal. Hence, substituting the above relations for W\ and Wt in the relations for W and PF", equating and solving for Fone obtains The minimum effective aperture width may now be obtained from the equation for W But where n is the index of refraction of the lens and r\ and YI the radii of the two faces of the lens. In this case, let r\ = rz\ hence for thin lenses, But Solving for V between these two equations,