calculate focal length of a spherical mirror from the following observation object distance u=(50.1+0.5)cm and image distance v=(20.1+0.2)cm.
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Explanation:
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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