11.9 RAY OPTICS 01- How to find the distance of image for convex mirror.

An object is placed at a distance of 6 cm from a convex mirror. If the focal length of a mirror is 12 cm find the position and nature of an image.



Given:
Distance of object = u = -6 cm (the -ve sign represents the object is placed at left side of the mirror.)

Focal length of mirror = f = 12 cm

Solution:-

using mirror equation we get
( 1 /  f ) = ( 1 / u ) + ( 1 / v )

therefore,

( 1/ v ) = (1 / f ) - ( 1 / u )

( 1/ v ) = (1 / 12  ) - ( 1 / - 6 )

( 1/ v ) = (1 / 12 ) + ( 1 / 6 )

( 1/ v ) = (1 / 12) + { ( 2 / 2) ( 1 / 6 ) }

( 1/ v ) = (1 / 12 ) + ( 2 / 12)

( 1/ v ) = (1 +2)/ 12

( 1/ v ) = 3 / 12

( 1 / v ) = (1 / 4 )

i.e.

v = 4 cm

In case of convex mirror, the image is always virtual, erect and diminished.....