# Cartesian Sign

Cartesian Sign Convention Conventions for showing object distance, image distance, focal length, etc. with suitably adding positive or negative signs before the measurement. The equation that shows relationship among object distance, image distance and focal lenght. Ratio between image size and object size, or between image distance and object distance.

## Sign Convention for Spherical Mirror:

Cartesian Sign Convention: In the case of spherical mirror all signs are taken from Pole of the spherical mirror, which is often called origin or origin point. This sign convention is known as New Cartesian Sign Convention.

Sign is taken as – (negative) from pole of a spherical mirror towards object along the principal axis. This means sign is always taken as – (negative) in front of a spherical mirror. For example; the distance of object is always taken as – (negative) in case of both types of spherical mirror, i.e. concave and convex mirrors.

• Sign is taken as + (positive) behind the spherical mirror. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis.
• The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.

Fig: Cartesian Sign Convention

• Since, object is always placed in front of the mirror hence object distance is taken as negative.
• Since, the centre of curvature and focus lie in front of the concave mirror, so radius of curvature and focal length are taken as negative in the case of concave mirror.
• When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).
• Height of image is taken as positive in the case of erect image and taken as negative in the case of inverted image.

• Since, object is always placed in front of the mirror hence object distance is taken as negative.
• Since, the centre of curvature and focus lies behind the convex mirror, so radius of curvature and focal length are taken as + (positive) in the case of convex mirror.
• In the case of convex mirror, image always formed behind the mirror, thus the distance of image is taken as positive.
• In the case of a convex mirror, always an erect image is formed, thus the height of image is taken as positive.

### Mirror Formula:

Mirror formula shows the relation among distance of object, distance of image and focal length in case of spherical mirror. All distances are measured from pole of the mirror.

The distance of object is denoted by u
The distance of image is denoted by v
Focal length is denoted by f

1/v+1/u=1/f

By knowing any two, the third can be calculated using the mirror formula.

#### Magnification:

Magnification is the relative ratio of size of image formed by a spherical mirror to the size of object. Magnification is generally denoted by letter ‘m’.

text(Magnification m)=text(Height of image h’)/text(Height of object h)

Or, m=(h_i)/(h_o)

Relation among magnification, distance of object and distance of image:

text(Magnification m)=text(Distance of image)/text(Distance of object)=-v/u

Thus, m=(h')/(h)=-v/u

Where; m = magnification, h' = height of image, h = height of object, v = image distance and u = object distance.