## sign convention for lenses

axis. The object is always placed on the left side of the lens. Cartesian sign conventions are used for measuring the various distances in the ray diagrams of spherical lenses. Lens Formula: Lens formula gives the relationship between ob distanceject (u), image-distance (v) and the focal length (f ). SIGN CONVENTION. Derivation of lens formula or mirror equation; Sign Conventions. So the thin lens formula equation ():$\frac 1 f= \frac 1 {s'}+\frac 1 s$ This will only give you correct results, if you follow the correct sign conventions. h . 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 For converging lenses, the focal length is always positive, while diverging lenses always have negative focal lengths. SIGN CONVENTION. New Cartesian Sign Convention is used to avoid confusion in understanding the ray directions. Sign convention - definition Object is always placed to the left of lens. The first time when sign convention is applied to derive Lens Formula, it is to make sure the formula is as general as possible. All the distances are measured from the optical centre of the lens. The distances measured in the direction of incident rays are positive and all the distances measured in the direction opposite to that of the incident rays are negative. Refer to the diagram for clear visualization. Sign conventions 4 • Light travels from left to right • A radius of curvature is positive if the surface is convex towards the left • Longitudinal distances are positive if pointing to the right • Lateral distances are positive if pointing up • Ray angles are positive if the ray direction is obtained by rotating the lenses, types of lens,sign of conventions of radius of curvature and principal focus All the distances are measured from the optical centre of the lens. 1. According to cartesian sign convention, 1. The sign convention is important in how you define your quantities. Following sign convention is used for measuring various distances during the formation of images by lenses: All distances on the principal axis are measured from the optical center. 2. Sign is taken as + (positive) behind the spherical mirror. All distances are measured from the optical centre of the mirror. However, these conventions are arbitrary, and physicists could just as easily have made the signs opposite. u, v, f, object height . We must take care to apply appropriate signs for the values of . According to it: Object is always placed to the left of lens. h ′. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis. The distances measured against the direction of incident light are taken as negative. and image height . 2. Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. 3. According to cartesian sign convention, 1. The sign conventions for the given quantities in the lens equation and magnification equations are as follows: f is + if the lens is a double convex lens (converging lens) f is - if the lens is a double concave lens (diverging lens) d i is + if the image is a real image and located on the opposite side of the lens. https://www.khanacademy.org/.../v/sign-conventions-for-mirror-lenses For the measurement of all the distances, the optical center of the lens is considered. The lens formula is expressed as, 1 = 1 3. The distances measured in the same direction as that of incident light are taken as positive. According to the convention, the focal length of a convex lens is positive and that ofa concave lens is negative. Figure of converging lens with labeled negative and positive focal lengths. The object is always placed on the left side of the lens. Cartesian sign conventions are used for measuring the various distances in the ray diagrams of spherical lenses. You missing an important point here: each time sign convention is applied, it has some purpose. Sign Convention for Spherical Lenses All the distances are measured from the optical center of the lens. If the vertex lies to the right of the center of curvature, the radius of curvature is negative. The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis. The sign convention for the optical radius of curvature is as follows: If the vertex lies to the left of the center of curvature, the radius of curvature is positive.

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