The objective lens of a compound microscope produces magnification of 10. In order to get an overall magnification of 100 when image is formed at `25cm` from the eye, the focal length of the eye lens should be

Options

A. 4 cm
B. 10 cm
C. `(25)/(9) cm `
D. 9 cm

Answer

C

Explanation

`m_(o) = 10 , m = 100`
`m = m_(o) (1 + (D)/(f_(e)) ) rArr 100 = 10 (1 + (D)/(f_(e)) ) `
`rArr 1 + (25)/(f_(e)) = 10 rArr (25)/(f_(e)) = 9 rArr f_(e) = (25)/(9) cm`.