A compound microscope has an eye piece of focal length `10 cm` and an objective of focal length `4 cm`. Calculate the magnifcation, if an object is kept at a distance of `5 cm` from the objective so that final image is formed at the least distance vision `(20 cm)`

Options

A. `12`
B. `11`
C. `10`
D. `13`

Answer

A

Explanation

Here, `u_(0)=-5` cm, `f_(0)=4` cm,
`f_(e)=10` cm, `D=20` cm
According to lens formula,
`(1)/(v_(0))-(1)/(u_(0))=(1)/(f_(0))` or `(1)/(v_(0))=(1)/(f_(0))+(1)/(u_(0))`
Substituting the given values, we get
`(1)/(v_(0))=(1)/(4)+(1)/(-5)=(1)/(4)-(1)/(5)=(1)/(20)impliesv_(0)=20` cm
Magnification, `M=(v_(0))/(|u_(0)|)(1+(D)/(f_(e)))=(20)/(5)(1+(20)/(10))=12` cm