Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometric optics, the paraxial approximation is a small-angle approximation used in ray tracing of light through an optical system (such as a lens).A paraxial ray is a ray which makes a small angle ( ) to the optical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for in radians) for calculation of the ray's path:In some cases, the second-order approximation is also called "paraxial". The approximations above for sine and tangent are already accurate to second order in , but the approximation for cosine needs to be expanded by including the next term in the Taylor series expansion. The third approximation then becomes

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