The graph between object distance `u` and image distance `v` for `a` lens is given below. The focal length of the lens is.
(a) `5 pm 0.1`
(b) `5 pm 0.05`
( c) `0.5 pm 0.1`
(d) `0.5 pm 0.05`.
.

Explanation

From the lens formula,
`1/f=1/v-1/u we have,`
`1/f=1/(10)-1/(-10)or f =
+5`
Further, `Deltau= 0.1`
and `Deltav=0.1`
Now, differentiating the lens formula, we have
`(Deltaf)/(f^2)=(Deltav)/(v^2)+(Deltau)/(u^2)`
or `(Deltaf)=((Deltav)/(v^2)+(Deltau)/(u^2))f^2`
Substituting the values, we have
`Deltaf =((0.1)/(10^2)+(0.1)/(10^2))(5)^2=0.05`
`:. f +- Deltaf = 5 +- 0.05`
`:.` The correct option is (b).