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The separation L between the objective (...

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.

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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.`
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