Sign Conventions For Lenses


 
 
Concept Explanation
 

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 u
From the optical centre to the image image-distance v
From the optical centre to second principal focus focal length f
Height of the object object-height h_{o}
Height of the image image-height h_{i}

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 h_{o} and h_{i} 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 (u,v,f,h_{o},h_{i}) 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

  • u,v and f are measured from the optical centre.
  • If a distance is measured along the incident rays, the corresponding quantity is positive. If a distance is measured opposite to the incident rays, the corresponding quantity is negative.
  • Coordinate Convention

       for h_{o},h_{i}

  • The object-height h_{o} is always taken as positive. If the image is formed on the same side of the principal axis (erect image), the image-height h_{i} is also positive. If the image is formed on the opposite side (inverted image), h_{i} is negative.
  • 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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