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A compound microscope consists of an obj...

A compound microscope consists of an objective of focal length 1.0 cm and an eyepiece of focal length 5.0 cm separated by 12.2 cm. At what distance from the objective should a object be placed to focus it properly so that the final image is formed at the least distance of clear vision (25cm)? b. calculate the angular magnification in this case.

Text Solution

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a. For the eyepiece `v_e=-25cm nd f_e=+5cm`
Using `1/v_e-1/u_e=1/f_e`
`1/u_e=1/v_e-1/f_e`
`-1/(25cm_-1/(5cm)`
or `u_e=25/6cm=-4.17=-4.2cm`
As the objective is 12.2 cm away from the eyepiece the image formed by the objective is 12.2 cm-4.2 cm =8.0 cm away from it. for the objective
`v=+8.0 cm, f_0=+1.0cm`
Using `1/v-1/u=1/f_0`
`1/u=1/v-1/f_0`
`=1/(8.0cm)-1/(1.0cm)`
or `u=-8.0/7.0cm=-1.1cm.`
b. The angular magnification is
`m=v/u(1+D/f_e)`
`=(+8.0cm)/(-1.1cm)(1+(25cm)/(5cm))=-44`.
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