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The eyepiece and objective of a microsco...

The eyepiece and objective of a microscope having focal lengths of 0.03 m and 0.04 m respectively are separated by a distance 0.2 m. Now the eyepiece and the objective are to be interchanged such that the angular magnification of the instrument remains the same. What is the separation between the lenses?

Text Solution

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Given data : In first case, `f_e = 0.03 m`
` f_0 = 0.04 m, L = 0.2 m`
In second case, `f_e = 0.04 m`
` f_0 = 0.03m, L = ? `
` m = (L)/(f_0) ( 1+ (0.25)/(f_e))`
for m to be same in the both cases
` = (L)/(0.03) ( 1+ (0.25)/(0.04))`
` = (0.2)/(0.04) ( 1+ (0.25)/(0.03))`
` = (L)/(0.03) xx 29/4 = (0.2)/(0.04) xx 28/3 `
`L = (5.6)/(29) = 0.193 m`
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