MENISCUS

, a lens or glass, convex on one side, and concave on the other. Sometimes also called a Lune or Lunula. See its figure under the article Lens.

To find the Focus of a Meniscus, the rule is, as the difference between the diameters of the convexity and concavity, is to either of them, so is the other diameter, to the focal length, or distance of the focus from the Meniscus. So that, having given the diameter of the convexity, it is easy to find that of the concavity, so as to remove the focus to any proposed distance from the Meniscus. For, if D and d be the diameters of the two sides, and f the focal distance; then since, by the rule , therefore , or .

Hence, if D the diameter of the concavity be double to d that of the convexity, f will be equal to D, or the focal distance equal to the diameter; and therefore the Meniscus will be equivalent to a planoconvex lens.

Again, if D = 3d, or the diameter of the concavity triple to that of the convexity, then will f = (1/2)D, or the focal distance equal to the radius of concavity; and therefore the Meniscus will be equivalent to a lens equally convex on either side.

But if D = 5d, then will f = (1/4)D; and therefore the Menlscus will be equivalent to a sphere.

Lastly, if D = d, then will f be infinite; and therefore a ray falling parallel to the axis, will still continue parallel to it after refraction.