New Cartesian sign convention is used for measuring the various distances in the ray diagram of spherical lenses(convex lenses and concave lenses).
According to the new Cartesian sign convention
- All the distance are measured from the optical centre of the lens.
- The distance measured in the same direction as that of incidence light are taken as positive.
- The distance measured against the direction of incident light are taken as negative.
- The distance measured upward are perpendicular to the principal axis are taken as positive.
- The distance measured downward and perpendicular to the principal axis taken as negative.
Lens Formula
A formula which gives the relationship between image distance(v), object distance(u), and focal length(f) of a lens is known as the lens formula.
Where v=image distance
u=object distance
f=focal length
Note:-It is clear that the mirror formula has a plus sigh(+) between 1/v and 1/u, whereas the lens formula has a minus sign (-) between 1/v and 1/u.
Magnification Produced by Lenses
The size of the image formed by a lens depends on the position of the object from the lens. The linear magnification is the ratio of the height of the image to the height of the object.
The linear magnification produced by a lens is equal to the ratio of image distance to the object distance
After equating both magnification, we got
Note:-The magnification formula from mirror has a minus(-) sign (m=-v/u) but the magnification formula for lens has positive (+) sign (m=v/u).