CBSE Class 12-science Answered

Magnification m of image formed by concave mirror is

m = - v / u = (  h_i / h_o )

where v is mirror-to-image distance and u is mirror-to-object distance .

where h_i = 3 cm is height of image and h_o =  2 cm is height of object .

Since image is virtual both heights of object and image are positive .

Hence magnification m is 

m = - v/u = 3/2 = 1.5

Mirror-to-object distance u =  -16 cm ( Cartesian sign convention is followed )

Hence mirror-to-image distance is

v = 16 × 1.5 = 24 cm

Focal length f is calculated from mirror equation

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

1/f = ( 1/24 ) - ( 1/16) = -1/48

Hence focal length of concave mirror = - 48 cm

( Focal length of concave mirror is negative by Cartesian sign convention )