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..
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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