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Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F1. When the space between the two lenses is filled with glycerin (which has the same refractive index (μ=1.5) as that of glass) then the equivalent focal length is F2. The ratio F1:F2 will be

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a
3 : 4
b
2 : 1
c
1 : 2
d
2 : 3

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detailed solution

Correct option is C

According to lens maker's formula  1f=(μ-1)1R1-1R2 1f=(μ-1)1R-1-R=(1.5-1)2R=1RTwo similar equi-convex lenses of focal length f each are held in contact with each other.The focal length F1 of the combination is given by1F1=1f+1f=2f; F1=f2=R2                   .........(i)For glycerin in between lenses, there are three lenses, one concave and two convexFocal length of the curve lens is given 1f'=(1.5-1)-2R=-1RNow, equivalent focal length of the combination is given by1F2=1f+1f'+1f;1F2=1R-1R+1R=1RF2=R                                                                      ..........(ii)  Dividing equation (i) by (ii), we get F1F2=12

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