An object placed 20cm in front of a mirror is found to have an image 15cm (a) in front of it, (b) behind the mirror . Find the focal length of the mirror and the kind of mirror in each case.
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CASE A
with sign convention
u= -20
v= -15
using mirror formula
1/v+1/u=1/f
-1/15-1/20 =1/f
-4-3/60=1/f
f= -60/7
since f is negative, therefore it is a concave mirror.
CASE B
U= -20
v= +15
using mirror formula
1/v+1/u= 1/ f
1/15-1/20=1/f
4-3/60=1/f
f=60
f is positive so it is a convex mirror
with sign convention
u= -20
v= -15
using mirror formula
1/v+1/u=1/f
-1/15-1/20 =1/f
-4-3/60=1/f
f= -60/7
since f is negative, therefore it is a concave mirror.
CASE B
U= -20
v= +15
using mirror formula
1/v+1/u= 1/ f
1/15-1/20=1/f
4-3/60=1/f
f=60
f is positive so it is a convex mirror
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