The focal length of the objective and eye lenses of a microscope are 1.6 cm and 2.5 cm respectively. The distance between the two lenses is 21.7 cm. If the final image is formed at infinity. What is the linear magnification ?

Options

A. 11
B. 110
C. `1.1`
D. 44

Answer

B

Explanation

Here `v_(O)=L-f_(e )=21.7 cm - 2.5 cm = + 19.2 cm`
`+ve` sign show that image is real.
For a objective lens `(1)/(u_(O))+(1)/(v_(O))=(1)/(f_(O))` [using real-virtual sign convention]
`therefore (1)/(u_(O))=(1)/(f_(O))+(1)/(v_(O)) therefore (1)/(u_(O))=(1)/((+1.6))-(1)/((+19.2))`
`(1)/(u_(O))=(19.2-1.6)/((1.6)(19.2))` or `u_(O)= +17.45 cm`
`+ve` sign show that object is real
When the image is formed at infinity, the magnification is given by
`m = ((v_(O))/(u_(O)))((D)/(f_(e )))`
where D is the distance of distinct vision.
`therefore m=((19.2 cm)/(1.745 cm))((25 cm)/(2.5 cm))=110`.