Question

Two similar plano-convex lenses are placed with their convex surfaces in contact and the space between them is filled with a liquid of refractive index $1.7$, as shown in figure. The focal length of plano-convex lens is $25cm$ and radius of curvature of the curved surface is $12.5cm$. The focal length of the combination is :

• A. $–31.25cm$
• B. $–42.05cm$
• C. $–37.73cm$
• D. $-52.65cm$

Answer 1

The correct option is A $–31.25cm$

The above setup can be considered as combination of three lens (two plano convex lens and one liquid lens)
Focal length of combination is given by
$\frac{1}{F_{eff}}=\frac{1}{f_l}+\frac{1}{f_{g1}}+\frac{1}{f_{g2}}$

Focal length of each plano-convex lens $f_{g1}=f_{g2}=25cm$ .
$Focallengthoftheliquidlensis\frac{1}{f_l}=(\mu -1)\left(\frac{-2}{\text{R}}\right)\frac{1}{f_l}=(1.7-1)\left(\frac{-2}{12.5}\right)\therefore f_l=\frac{-125}{14}cmEffectivefocallengthofcombinationis\frac{1}{F_{eff}}=\frac{1}{f_l}+\frac{1}{f_{g1}}+\frac{1}{f_{g2}}=+\frac{2}{25}-\frac{14}{125}\therefore {\text{F}}_{eff}=\frac{-125}{4}=-31.25cm$