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 $F_{1}$ . When the space between the two lenses is filled with glycerine (which has the same refractive index ( $μ = 1.5$ ) as that of glass) then the equivalent focal length is $F_{2}$ . The ratio $F_{1} : F_{2}$ will be :

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Answer 1

Equivalent focal length in air,
$\frac{1}{F _{1}} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$
When glycerin is filled inside, glycerin lens behaves like a diverging lens of focal length (-f)
$⟹ \frac{1}{F _{2}} = \frac{1}{f} + \frac{1}{f} - \frac{1}{f}$
$= \frac{1}{f}$
$⟹ \frac{F _{1}}{F _{2}} = \frac{1}{2}$

Answer 2

Equivalent focal length in air,

\frac{1}{F _{1}} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}

When glycerin is filled inside, glycerin lens behaves like a diverging lens of focal length (-f)

⟹ \frac{1}{F _{2}} = \frac{1}{f} + \frac{1}{f} - \frac{1}{f}

= \frac{1}{f}

⟹ \frac{F _{1}}{F _{2}} = \frac{1}{2}