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 25 cm and radius of curvature of the curved surface is 12.5 cm and is made of glass of refractive index 1.5. The focal length of the combination is :

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

Answer 1

The correct option is A – 31.25 cm

Focal length of each plano-convex lens = 25 cm. Focal length of glass lens is $\frac{1}{f_g}=2\times \frac{1}{25}=\frac{2}{25}\Rightarrow f_g=\frac{25}{2}cmFocallengthoftheliquidlensis\frac{1}{f_l}=(\mu -1)\left(\frac{-2}{\text{R}}\right)\frac{1}{f_l}==(1.7-1)\left(\frac{-2}{12.5}\right)\therefore f_l=\frac{-125}{14}Effectivefocallengthofcombinationis\frac{1}{F_{eff}}=\frac{1}{f_l}+\frac{1}{f_l}=+\frac{2}{25}-\frac{14}{125}\therefore {\text{F}}_{eff}=\frac{-125}{4}=-31.25cm$