Solid angle orientation formula_9, and distance from the viewer as: where the surface area of a sphere is . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2, is the area of a spherical cap on a unit sphere For small such that , this reduces to the area of a circle . The above is found by computing the following double integral using the unit surface element in spherical coordinates: This formula can also be derived without the use of calculus. Over 2200 years ago Archimedes proved that the
Surface modification the surface of solid matter. It has applications to chemistry, mechanical engineering, and electrical engineering (particularly in relation to semiconductor manufacturing). Solids are composed of a bulk material covered by a surface. The surface which bounds the bulk material is called the Surface phase. It acts as an interface to the surrounding environment. The bulk material in a solid is called the Bulk phase. The surface phase of a solid interacts with the surrounding environment. This interaction can degrade the surface phase over time. Environmental degradation of the surface phase over time can be caused by wear, corrosion, fatigue and