12. Lens formula and Sign convention

We use the same sign convention for lenses as we do for spherical mirrors. We use the same rules for distance signs, except that all measurements are taken from the lens's optical centre. According to the convention, the focal length of a convex lens is positive, while that of a concave lens is negative. For the values of \(u\), \(v\), \(f\), object height h, and image height \(h′\), you must use appropriate signs.

 

 

We have a formula for spherical lenses, just as we do for spherical mirrors. This formula gives the relationship between object distance (\(u\)), image distance (\(v\)) and the focal length (\(f\)). The lens formula is expressed as

 

The lens formula given above is general and is valid in all situations for any spherical lens. Take proper care of the signs of different quantities while putting numerical values for solving problems relating to lenses.

 

Sign convention:

 

The various distances in the ray diagrams of spherical lenses are measured using Cartesian sign conventions. According to the convention of cartesian signs,
1. The object is always positioned on the lens's left side.
2. All distances are measured from the lens' optical centre.
3. Positive distances are those measured in the same direction as the incident light.
4. Negative distances are those measured in the opposite direction of incident light.
5. Positive distances are those measured upward and perpendicular to the principal axis.
6. Negative values are assigned to distances measured downward and perpendicular to the principal axis.