The focal length of the object glass of a microscope is 2 cm, that of the eye-piece is 4 cm and the distance between them is 20 cm. What should be the object distance from object glass if the final image is to be seen at least distance of distinct vision (25 cm) from the eyepiece? What will be the magnification in this situation ?

48

Let the required distance be x cm

For eye piece,

$=-\frac{1}{25}-\frac{1}{u_e}=\frac{1}{4}⇒u_e=-\frac{100}{29}cm$

⇒ Image distance for objective = $(20 -\frac{100}{29}) cm = \frac{480}{29}cm$.

$\frac{29}{480}-\frac{1}{x}=\frac{1}{2}⇒x=\frac{480}{211}cm$

Required magnification $M=\frac{211}{29}(1+\frac{25}{4})=48$