Question

The radius of curvature of concave mirror is 60 cm and the object distance is 60 cm then its image distance is_

Answer 1

r=-60
f=r/2
f=-30
u=-60
v=?
1/v+1/u=1/f
1/v+1/-60=1/-30
1/v=1/60-1/30
=1-2/60
=-1/60
so
v=-60

Answer 2

object distance (U)=60cm

radius of curvature(R)=60cm

⇒focal lenth(F)=R/2=30cm

but given mirror is concave mirror.

after using the sign conventions,

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u=-60cm

f=-30cm

now image distance (V)=-v=?

by using mirror formula,

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1/f = 1/v -1/u

1/-30 = 1/-v - 1/-60

1/-30 = 1/-v +  1/60

1/-v = 1/-30 - 1/60

1/-v=1*2/-30*2 - 1/60

1/-v=2-1/60

1/-v=1/60

-v = 60

v = -60 cm

∴the image distance is -60 cm.

the nature of the image is real , inverted , same size.