. 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.
Best Answer
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.
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