Q1. In an experiment to measure focal length $( f )$ of convex lens, the least counts of the measuring scales for the position of object $( \mathrm { u } )$ and for the position of image $( \mathrm { v } )$ are $\Delta \mathrm { u }$ and $\Delta \mathrm { v }$, respectively. The error in the measurement of the focal length of the convex lens will be: (1) $2 f \left[ \frac { \Delta \mathrm { u } } { \mathrm { u } } + \frac { \Delta \mathrm { v } } { \mathrm { v } } \right]$ (2) $\frac { \Delta u } { u } + \frac { \Delta v } { v }$ (3) $f ^ { 2 } \left[ \frac { \Delta \mathrm { u } } { \mathrm { u } ^ { 2 } } + \frac { \Delta \mathrm { v } } { \mathrm { v } ^ { 2 } } \right]$ (4) $f \left[ \frac { \Delta \mathrm { u } } { \mathrm { u } } + \frac { \Delta \mathrm { v } } { \mathrm { v } } \right]$
Q1. In an experiment to measure focal length $( f )$ of convex lens, the least counts of the measuring scales for the position of object $( \mathrm { u } )$ and for the position of image $( \mathrm { v } )$ are $\Delta \mathrm { u }$ and $\Delta \mathrm { v }$, respectively. The error in the measurement of the focal length of the convex lens will be:\\
(1) $2 f \left[ \frac { \Delta \mathrm { u } } { \mathrm { u } } + \frac { \Delta \mathrm { v } } { \mathrm { v } } \right]$\\
(2) $\frac { \Delta u } { u } + \frac { \Delta v } { v }$\\
(3) $f ^ { 2 } \left[ \frac { \Delta \mathrm { u } } { \mathrm { u } ^ { 2 } } + \frac { \Delta \mathrm { v } } { \mathrm { v } ^ { 2 } } \right]$\\
(4) $f \left[ \frac { \Delta \mathrm { u } } { \mathrm { u } } + \frac { \Delta \mathrm { v } } { \mathrm { v } } \right]$