# . List the new Cartesian sign convention for reflection of light by spherical mirrors

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.

Ans. New Cartesian Sign Conventions for spherical mirrors.

Sign conventions for reflection of light by spherical mirrors.

(i) All the distances are measured from pole of the mirror as origin.

(ii) The object is always placed to the left of the mirror. ,

(iii) Distances measured in the direction of incident light are considered to be positive (+ve).

(iv) Distances  measured  against  the  direction  of  incident  light  are  considered  to  be negative (-ve).

(v) The  perpendicular  distances  to  the  principal  axis  in  the  upward   direction  are considered  to be positive (+ve).

(vi) The perpendicular distances to the  principal  axis in  the downward direction  are considered to be negative (-ve).

u = object distance v = image distance

h = height of the object      h' = height of the image

P =Principal axis C = Centre of curvature

f = focal length       F =Focus Diagram. When the object is between F and C (centre of curvature): The image formed is

(i) real

(ii) inverted

(iii) magnified

(iv) beyond C.

PA = Object distance = This distance lies in the direction opposite to the incident ray

:. PA, i.e., u = -16

Magnification is 3 times : m = 3 The negative (-) sign of focal length shows that it is a concave lens  of focal length 12 cm.

F = ?  Nature of spherical mirror = ?

The image is 1/3 times magnified and virtual

Magnification, m = + 1/3

U = -18 cm   (+ve sign of m is for virtual image) Positive (+) sign of shows that the spherical mirror is convex having  focal length of 9 cm.