Q.

The focal length of a mirror is given by 1v1u=2f. If equal errors are made in measuring u and v, then the relative error in f, is

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a

α1u1v

b

α1u+1v

c

2α

d

none of these

answer is B.

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Detailed Solution

We have,

    1v1u=2f    d1v1u=d2f    1v2dv+1u2du=2f2df    1v21u2α=2f2df    α1v+1u1v1u=2f2df    α1v+1u×2f=2f2df                                               1v1u=2f    dff=α1u+1v[ du=dv=α]

 Relative error in f=α1u+1v

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The focal length of a mirror is given by 1v−1u=2f. If equal errors are made in measuring u and v, then the relative error in f, is