Sign Conventions For Lenses
Sign Conventions For Lenses
With thin lenses, we generally come across three distances parallel to and two distances perpendicular to the principal axis. Each of these distances we define a particular quantity and a symbol is assigned to it. These quantities are given in table.
| Distance | Quantity | Symbol |
| From the optical centre to the object | object-distance | |
| From the optical centre to the image | image-distance | |
| From the optical centre to second principal focus | focal length | |
| Height of the object | object-height | |
| Height of the image | image-height |
The above definitions of u and v are for a point object placed on the principal axis. If an object is placed away from the principal axis, u corresponds to the distance from the optical centre to the foot of the perpendicular drawn from the object to the principal axis. Similarly, v corresponds to the distance from the optical centre to the foot of the perpendicular drawn from the image to the principal axis. The quantities and
are defined for a linear, extended object placed perpendicular to the principal axis.
For finding a particular distance when some other are given, we need to assign these quantities positive or negative signs according to a fixed set of rules, or a convention. Several conventions for the signs of these quantities are in use. We shall follow the Cartesian coordinates convention.
1 Transverse distances are measured from the optical centre.If the object or image is present above the principal axis than it is taken as positive that is positive y axis while those are below taken as negative that is negative y axis.
2 Longitudinal distances are also measured from the optical centre and taken as positive if they are in the direction of propagation of incident light that is positive x axis and taken as negative if they are in opposite direction that is negative x-axis..
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Coordinate convention For u, v, f |
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Coordinate Convention for |
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Note that in this convention, f is negative for a concave lens and positive for a convex lens. Also, heights above the principal axis are positive and those below it are negative.
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