Figure \(\PageIndex{2b}\) shows a spherical mirror that is large compared with its radius of curvature. The new Cartesian sign convention is used for measuring the various distances in the ray-diagrams of spherical mirrors. In this convention, the pole (P) of the mirror is taken as the origin. The following sign conventions are used by Cartesian: (1) All distances are measured from the pole of the mirror (in the case of the lens from the optic center). The table below shows object and image distances for four objects placed in front of mirrors. Sign convention for reflection by spherical mirrors. is the sag—the z-component of the displacement of the surface from the vertex, at distance Refer to the diagram for clear visualization. New Cartesian Sign Convention is used for measuring the various distances in the ray diagrams of spherical mirrors. For which one is the image formed by a convex spherical mirror? Spherical Mirror Equation. Light | Sign Convention of Mirrors | CBSE Class 10 Physics NCERT Solutions | Umang Vedantu Class 9 and 10. [Positive and negative signs are used in accordance with standard sign convention] The principal axis of the mirror is taken as the x … We can see the sign convention in both mirrors Some points to note Since focus of concave mirror is on the left side (in front of the mirror) , Focal length of concave mirror is negative Since focus of convex mirror is on the right side (behind the mirror), Focal length of convex mirror is positive 2.All distances are measured from the pole of a spherical mirror. New Cartesian Sign Convention is used to avoid confusion in understanding the ray directions. 3.The distance measured in the direction of the incident light are taken as positive and those measure in a direction opposite to the direction of incident light are taken as negative. b-Trace the path of the reflected ray by drawing a figure if it passes from the center of curvature of a conacve mirror This sign convention is known as New Cartesian Sign Convention. Sign convention for reflection by spherical mirrors Reflection of light by spherical mirrors follow a set of sign conventions called the New Cartesian Sign Convention. According to New Cartesian Sign Convention: The new Cartesian sign convention is used while considering different terms for reflection through spherical mirrors. Sign convention for Spherical Mirrors. According to the new Cartesian sign convention (figure 1) : (i) The pole ‘P’ of the mirror is taken as the origin and the principal axis of the mirror is taken as the x-axis of the coordinate system. The equation for image formation by rays near the optic axis (paraxial rays) of a mirror has the same form as the thin lens equation if the cartesian sign convention is used:. From the geometry of the spherical mirror, note that the focal length is half the radius of curvature: This means the sign is always taken as −(negative) in front of a spherical mirror. Draw a diagram and apply these conventions for calculating the focal length and nature of spherical mirror which forms a 1/3 times magnified virtual image of an object placed 18 cm in front of it. The modern cartesian sign conventions are: 1.An object is always placed to the left of a mirror. The principal axis of the mirror is taken as the x-axis (X'X) of the coordinate system. 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