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Questions  

The focal length of a spherical mirror from the following observations : object distance u=50.1±0.5  cm and image distance v=20.1±0.2 cm is

a
14.3±0.2 cm
b
14.3±0.1 cm
c
14.3±0.4 cm
d
14.3±0.3 cm

detailed solution

Correct option is B

GivenObject distance u=u±Δu=50.1±0.5 cmImage distance  v=v±Δv=20.1±0.2 cmFrom mirror formula1F=1v+1u ⇒1F=150.1+120.1∴F=14.34 cmand ΔFF2=Δvv2+Δuu2⇒ΔF=ΔuFu2+ΔvFv2=0.514.3450.12+0.214.3420.12=0.04+0.10=0.14 cmHence, F=14.3±0.1 cm

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