The separation L between the objective `(f=0.5cm()` and the eyepiece (f=5cm) of a compound microscope is 7 cm. Where should a small object be placed so that the eye is least strained to see the image? Find the angular magnification produced by the microscope.

Explanation

The eye is least strain dif the fiN/Al image is formed at infinity. In such a case, the image formed by the objective should fal at the focus of the eyepiece. As `f_e=5 and L=7` cm, this first image shold be formed at 7 cm -5cm=2cm from the objective. Thus, `v=+2. Also f_0=0.5` cm for the objective using
`1/v-1/u=1/f_0`
`1/u=1/v-1/f_0`
`=1/(2cm)-1/(0.5cm)`
or `u=-2/3cm

the angular magnification in this case is
`m=v/u D/f_0`
`=(2cm)/((2/3)cm)=(25cm)/(5cm)-15.`