Question

Focal length of the objective and the eyepiece in a microscope is 1 cm and 5 cm respectively. An object is 1.1 cm away from the objective and its final image forms at infinity. What is the length of the microscope and what is its magnification ?

Answer 1

a/c to question,

focal length of objective,$f_0$ = 1cm

focal length of eyepiece, $f_e$ = 5cm

object distance from the objective, $u_0$ = - 1.1cm


use formula, $\frac{1}{f_0}=\frac{1}{v_0}-\frac{1}{u_0}$

or, $\frac{1}{v_0}=\frac{1}{f_0}+\frac{1}{u_0}$

= 1/1 + 1/-6 = 6/6 - 1/6 = 5/6 cm

hence, $v_0$ = 6/5cm = 1.2cm

length of tube , L = $v_0+f_e$
= 1.2 cm + 5cm = 6.2cm

magnification , M = $\frac{v_0}{u_0}\left(1+\frac{D}{f_e}\right)$
= 1.2/-1.1(1 + 25cm/5cm)
= -1(1 + 5) =-6