List the cartesian sign convention for reflection of light by spherical mirrors. Draw a diagram and apply these conventions for calculating focal length and nature of a spherical mirror which forms a 1/3 times magnified virtual image of an object placed 18 cm in front of it.



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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 + (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.
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From pole to the (+ x-axis ) is taken as positive and from pole to ( - y - axis ) is taken as negative and from perpendicular to + y axis is taken as posittve