# How to use Focal-lengths in a sentence

focal-lengths
• A volume entitled Opera posthuma (Leiden, 1703) contained his "Dioptrica," in which the ratio between the respective focal lengths of object-glass and eye-glass is given as the measure of magnifying power, together with the shorter essays De vitris figurandis, De corona et parheliis, &c. An early tract De ratiociniis tin ludo aleae, printed in 16J7 with Schooten's Exercitationes mathematicae, is notable as one of the first formal treatises on the theory of probabilities; nor should his investigations of the properties of the cissoid, logarithmic and catenary curves be left unnoticed.

• The magnifying power of the telescope is = Ff /ex, where F and f are respectively the focal lengths of the large and the small mirror, e the focal length of the eye-piece, and x the distance between the principal foci of the two mirrors (=Ff in the diagram) when the instrument is in adjustment for viewing distant objects.

• Should there be in two lenses in contact the same focal lengths for three colours a, b, and c, i.e.

• Since the lens is bounded by air, the imageand object-side focal lengths f' and f are equal.

• Doublets, &'c. - To remove the errors which the above lenses showed, particularly when very short focal lengths were in question, lens combinations were adopted.

• A series of objectives with short focal lengths are available, which permit the placing of a liquid between the cover-slip and the front lens of the objective; such lenses are known as " immersion systems "; objectives bounded on both sides by air are called " dry systems."

• Beck, which can be conveniently fitted in and used for objectives with different focal lengths.

• The magnification of a microscope is determined from the focal lengths of the two optical systems and the optical tube length, for N = 250 A/fi'f2 To determine the optical tube length 0, it is necessary to know the position of the focal planes of the objective and of the ocular.

• For relatively short focal lengths a triple construction such as this is almost necessary in order to obtain an objective free from aberration of the 3rd order, and it might be thought at first that, given the closest attainable degree of rationality between the colour dispersions of the two glasses employed, which we will call crown and flint, it would be impossible to devise another form of triple objective, by retaining the same flint glass, but adopting two sorts of crown instead of only one, which would have its secondary spectrum very much further reduced.

• In the Ramsden eyepiece (see Microscope) the focal lengths of the two piano-convex lenses are equal, and their convexities are turned towards one another.