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

2

Explanation

Here `V_(0)` =L-`f_(c)` = 21.7 cm-2.5 cm = + 19.2 cm + ve sing show that image is real.
For a objective lens `1/u_(0) + 1/v_(0) = 1/f_(0)`
`:. 1/u_(0)=1/f_(0)-1/v_(0) :.1/u_(0)=1/(+1.6)-1/(19.2)`
`1/u_(0) = (19.2-1.6)/((1.6)(19.2))` or `u_(0) = +1.745` cm
[using real-virtual sign convention]
When the image is formed at infinity, the magnification is given by
m = `(v_(0)/u_(0)) (D/f_(e))`
where D is the distance of distinct vision. ltbr m=`(19.2cm)/(1.745cm)((25cm)/(2.5cm))`=110