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. The focal length of the combination is :

A
31.25 cm
B
42.05 cm
C
37.73 cm
D
52.65 cm

Solution

## The correct option is A –31.25 cmThe 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  1Feff=1fl+1fg1+1fg2 Focal length of each plano-convex lens fg1=fg2=25 cm .    Focallengthoftheliquidlensis1fl=(μ−1)(−2R)1fl=(1.7−1)(−212.5)∴fl=−12514 cmEffectivefocallengthofcombinationis1Feff=1fl+1fg1+1fg2=+225−14125∴Feff=−1254=−31.25 cm

Suggest corrections