Two similar thin equi-convex lenses, of focal length f each, are kept co-axially in contact with each other such that the focal length of the combination is 
. When the space between the two lenses is filled with glycerine (which has the same refractive index ( 
) as that of glass) then the equivalent focal length is 
. The ratio 
will be [NEET 2019]
Text Solution
Verified by ExpertsA
Case I When two equi-convex lens of focal length 
and 
respectively, are kept co-axially in contact, then the equivalent focal length of combination is
…… .. (i)
Case II When glycerine of same refractive index as that of the glass is filled in the space between two lens, then the combination will now comprises of three lenses; first bi-convex, second bi-concave and third is bi-convex.
So, the focal length of the combination now is given as
… . (ii)
From Eqs. (i) and (ii), we get
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