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A telescope has an objective of focal le...

A telescope has an objective of focal length `50cm` and an eyepiece of focal length `5cm.` The least distance of distinct vision is `25cm.` The telescope is focused for distinct vision on a scale `2m` away from the objective. Calculate (a) magnification produced and (b) separation between objective and eyepiece.

Text Solution

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Given `f_0=50cm and f_e=5cm`
For objective `1/v_0-1/-200=1/50 therefore 1/v_0=200/3 cm`
`m_0=v_0/u_0=((200//3))/(-200)=-1/3`
For eyepiece `1/-25 -1/u_e= 1/5`
`therefore u_e=25/6 cm and m_e=v_e/u_e=(-25)/(-(25//6))=6`
a) magnification m=`m_0 times m_e=-2`
b) Separation between objective and eyepiece,
`L=v_0+|u_e|=200/3+25/6=425/6=70.83cm`
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