Convex curve has at least four vertices, points that are local minima or local maxima of curvature. A curve "C" is convex if and only if there are no three different points in "C" such that the tangents in these points are parallel. Proof: ⇒ If there are three parallel tangents, then one of them, say "L", must be between the other two. This means that "C" lies on both sides of "L", so it cannot be convex. ⇐ If "C" is not convex, then by definition there is point "p" on "C" such that the tangent line at "p" (call it
Cylindrical lens Cylindrical lens A cylindrical lens is a lens which focuses light into a line instead of a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it into a line parallel to the intersection of the surface of the lens and a plane tangent to it. The lens compresses the image in the direction perpendicular to this line, and leaves it unaltered in the direction parallel to it (in the tangent plane). In a light sheet microscope, a cylindrical lens is placed in