Imaging Nearby Objects: Vergence and the Vergence Equation
If the source object is located only a finite distance to the left of a convex lens, but at greater distance than the focal length, f, the image will be farther to the right of the lens than the image of an object that is infinitely far away, such as a star. The distance from the source object to the lens is referred to as the object distance; the distance from the lens to the image is known as the image distance. Assuming both the source object and the image are in air, the formula for locating the image is
Figure I-9 The vergence equation: the object distance is u, the image distance is v, and the power of the lens is P.
U + P = V
where U = 1/u is the vergence of the object at a distance u to the left of the lens, P is the power of the lens, and V = 1/v is the vergence of the light emerging from the lens to form the image at distance v to the right of the lens (Figure I-9). Note: In this vergence equation, distances to the LEFT of the lens are treated as negative numbers (so, in this situation, u < 0). The vergence, U = 1/u, of an object to the left of a lens is likewise a negative number. Distances to the RIGHT of a lens, and thus, in this case, the image vergence V = 1/v, are considered positive. In this context, it is important to keep track of the sign of the power of a convex lens as a positive number as well. Objects infinitely far from the lens generate beams of light that reach the lens with a vergence of V = 1/∞ = 0.
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.