The focal length (f) of a spherical mirror is the distance between the pole and the principal focus. It is represented by the letter f and provides a quantitative measure of the mirror’s ability to converge or diverge light rays.
What is the focal length of a spherical mirror, and how is it defined in terms of the principal focus and the pole of the mirror?
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The focal length (f) of a spherical mirror is the distance between its principal focus (F) and its pole (P) along the principal axis. In concave mirrors, where the principal focus is on the same side as the incident light, the focal length is considered positive. For convex mirrors, where the virtual focus is on the opposite side of the mirror, the focal length is considered negative. Mathematically, the focal length is represented as f = PF. Understanding the focal length is crucial for predicting and analyzing image formation, magnification, and optical properties of spherical mirrors.
The focal length of a spherical mirror, denoted as ‘f,’ is the distance between the mirror’s principal focus (F) and its pole (P). For concave mirrors, where light converges, the focal length is considered positive, as the principal focus is real and located in front of the mirror. Conversely, for convex mirrors, where light diverges, the focal length is negative, and the principal focus is virtual, seemingly located behind the mirror. Mathematically, the relationship is defined as follows: f =PF, where ‘P’ is the pole, ‘F’ is the principal focus, and ‘f’ represents the focal length. Understanding the focal length is essential in optical design, enabling precise calculations for image formation and analysis in various optical systems.