In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are u and v, respectively. The error in the measurement of the focal length of the convex lens will be:
- 2f [ uu+ vv ]
- f [ uu+ vv ]
- f2 [ uu2+ vv2 ]
- uu+ vv
Answer
(3) f2 [ uu2+ vv2 ]
Solution
Lens formula: 1f= 1v- 1u
Differentiate: - dff2=- dvv2+ duu2
maximum error = sum of magnitudes of the errors:
ff2= uu2+ vv2
f=f2 [ uu2+ vv2 ]
Answer: (3)