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You are given two converging lenses of f...

You are given two converging lenses of focal lengths 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

Text Solution

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Formula : The magnification due to the objective lens diverging lens,
` m_0 = (v_0)/( - u_0)`
If the object is close to focus of the objective lens then
` mu_0 = f_0 " and " v = L`
(L = distance between two lenses)
` m_0 = (L)/(f_0)`
If the final image is at the near point, then magnification due to eye lens is
`m_e = ( 1 + D/f_e)`
`M = m_0 xx m_e = (L)/(f_0)( 1+ (D)/(f_e))`
Use ` f_0 = 1.25` cm and ` f_e = 5cm`
` 30 = (L)/(1.25) ( 1+ 25/5)`
` 30 = (L)/(1.25) xx 6 rArr L = (30 xx 1.25)/( 6) = 6.25 cm`
Separation between two lenses is 6.25 cm.
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