In a given optical bench, a needle of length 10 cm is used to estimate bench error. The object needle, image neddle & lens holder have their reading as shown. `X_(0) = 1.1 cm , X_(1) = 0.8 cm , X_(L) = 10.9 cm`
Estimate the bench error which are present in image neddle holder and object needle holder. Also find the focal length of the convex lens when `X_(0)= 0.6 cm , X_(1) = 22.5 cm , X_(L) = 11.4 cm`

Answer

`5.5 pm 0.05 cm`

Explanation

Index (Bench) error
= observed distance = Actual distance
`= (x_(L)-x_(o))-10cm=-0.2cm`
`u=(x_(L)-x_(o))-(-0.2)=10.8-(-0.2)=11cm`
`v=(x_(L)-x_(o))-(0.2)=22.5=11.4-0.2=10.9cm`
`(1)/(f)=(1)/(v)=(1)/(u)=(1)/(10.9)-(1)/(-11)rArrf=5.5cm` and
`(Deltaf)/(f^(2))=(Deltau)/(u^(2))+(Deltav)/(v^(2))rArr Deltaf=[(0.1)/((11)^(2))+(0.1)/((10.9)^(2))][5.5]^(2)=0.05`
`rArr f=(5.5 pm 0.05)cm`