12. What will be focal length of a spherical mirror if distance of object
from the mirror is (30 +0.5) cm and distance of image from the mirror is
(10 +0.2) em?
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ANSWER
Let focal length of the mirror be f cm.
v
1
+
u
1
=
f
1
20.1
1
+
50.1
1
=
f
1
⟹f=14.3 cm
As, f=
u+v
uv
∴ Taking log and differentiating, we get Δf=f(
u
Δu
+
v
Δv
+
u+v
Δu+Δv
)
Δf=14.3(
50.1
0.5
+
20.1
0.2
+
50.1+20.1
0.5+0.2
)=0.4 cm
Thus focal length of the mirror =(14.3±0.4) cm
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