An optical bench, to measure the focal length of lens, is 1.5 m long and on the bench marks are with spacing `1/4 cm`. Now a lens is placed at 75 cm and pin type object is placed at 45 cm marks on the bench. If its image is formed at 135 cm find maximum possible error in calculation of focal length.

Answer

1.38 & 1.39

Explanation

`u=(x_(2)-x_(1))=75-45=30cm`
`Deltau=Deltax_(2)+Deltax_(1)=1/4+1/4=1/2 cm`
`v=(x_(3)-x_(2))=135-75=60 cm `
`Deltav=Deltax_(3) +Deltax_(2) =1/4+1/4 =1/2 cm`
`:. 1/v-1/u=1/f implies 1/60 +1/30 =1/f`
`:.f=20 cm " " "Also" , (-dv)/(v^(2))+(-du)/(u^(2)) =(-df)/(f^(2))`
`implies (df)/f=f[(dv)(v^(2))+(du)/(u^(2))]=20[1/(60^(2))+1/(30^(2))]1/2`
`:. (df)/fxx100=10[1/36+1/9] =50/36 =1.38 & 1.39 ` (both)