List the new Cartesian sign convention for reflection of light by spherical mirrors. Draw a diagram and apply these conventions for calculating the 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.

List the new Cartesian sign convention for reflection of light by sphe

1.	List the new Cartesian sign convention for reflection of light by spherical mirrors. Draw a diagram and apply these conventions for calculating the 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.
Answer» Solution :For new CARTESIAN sign convention for reflection of LIGHT by SPHERICAL mirror, see Point NUMBER 15 under the heading "Chapter At A Glance". As per question and using the sign convention followed u = - 18 cm and magnification `m = + (1)/(3)` `therefore""m = - (v)/(u) = + (1)/(3)` `rArr""v = - (u)/(3) = - ((-18))/(3) = + 6` cm `therefore""(1)/(f) = (1)/(v) + (1)/(u) = (1)/((+6)) + (1)/((-18)) = (3-1)/(18) = (2)/(18) = (1)/(9)` `rArr""f = + 9` cm The +ve sign of .f. signifies that the mirror is a convex mirror. The ray diagram is shown in Figure.