# Sign convention for spherical lenses class 10 | cbse24

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.

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

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.

$magnification=\frac{height.of.image}{height.of.object}$

$m=\frac{h_{i}}{h_{o}}$

The linear magnification produced by a lens is equal to the ratio of image distance to the object distance

$Magnification=\frac{Image.distance}{Object.distance}$

$m=\frac{v}{u}$

After equating both magnification, we got

$m=\frac{v}{u}=\frac{h_{i}}{h_{o}}$

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).

*