Question

Focal length of a spherical mirror if u=50.1+-0.5 and v=20.1+-0.2

Answer 1

Calculate the focal length of a spherical mirror if measured quantities u and v are as folllows .


u=50.1+ or - 0.5 cm 


v=20.1+ or - 0.2 cm

Answer 2

Given data specifies about the v ±$\delta v$ and u ± $\delta u$. The formula to calculate the focal length of the spherical mirror is the

                   $\frac { 1 }{ f } =\frac { 1 }{ v } +\frac { 1 }{ u }$

Putting the values we simply get,

$\frac { 1 }{ f } =\frac { 1 }{ v } +\frac { 1 }{ u } =\frac { 1 }{ 50.1 } +\frac { 1 }{ 20.1 }$

$= \frac { 1 }{ 0.0697 } =14.34 cm$

For the $\delta f$ value we calculate through the formula delta

$\frac { \Delta f }{ f } =\frac { \Delta u }{ u } +\frac { \Delta v }{ v }$

$\Delta f=\quad f\left( \frac { \Delta u }{ u } +\frac { \Delta v }{ v }  \right)$

Putting the values, we get, delta

$\Delta f = 14.34 (0.00497+0.00399)$

$\Delta f  = 0.13.$

Therefore the focal length of the spherical mirror is $14.34 \pm  0.13cm$