1.

In `u-v` method to find focal length of a concave mirror, if object distance is found to be `10.0 cm` and image distance was also found to be `10.0 cm`, then find maximum permissible error in (f).

Answer» Correct Answer - C
Using the mirror formula,
`1/v+1/u=1/f`
we have, `1/(-10)+1/(-10)=1/f`
`rArr f=-5` or `|f|=5 cm`
Now, differentiating Eq. (i).
we have, `(-df)/(f^2)=-(du)/(u^2)-(dv)/(v^2)`
This equation can be written as
`|Deltaf|_(max)=[(|Deltau|)/(u^2)+(|Deltav|)/(v^2)](f^2)`
Substituting the values we get,
`|Deltaf|_(max)=[(0.1)/((10)^2)+(0.1)/((10)^2)](5)^2=0.05 cm`
`:. |f|=(5+- 0.05)cm`.


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