The focal length of a mirror is given by 1/f=1/u+1/v where u and v represent object and image distances respectively,The maximum relative error in f is ?
1 Answer
Feb 23, 2018
Given expression is
1/f=1/u+1/v
=>1/f=(v+u)/(uv)
=>f=(uv)(v+u)^-1
Taking
logf=logu+logv+log(v+u)^-1
=>logf=logu+logv-log(v+u)
Differentiating with respect to each variable.
(Deltaf)/f=(Deltau)/u+-(Deltav)/v+-(Delta(u+v))/(v+u)
HereDeltaf represents error inf and so on. It is assumed that errors in each are independent, random, and sufficiently small
=>(Deltaf)/f=(Deltau)/u+-(Deltav)/v+-(Deltau+Deltav)/(v+u)
=>(Deltaf)/f=(Deltau)/u+-(Deltav)/v+-(Deltau)/(v+u)+-(Deltav)/(v+u)
We calculate maximum average error as below