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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 :


Correct Answer
A
31.25 cm
Your Answer
B
42.05 cm
Your Answer
C
37.73 cm
Your Answer
D
52.65 cm

Solution

The correct option is A 31.25 cm
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 
1Feff=1fl+1fg1+1fg2

Focal length of each plano-convex lens fg1=fg2=25 cm . 
  Focallengthoftheliquidlensis1fl=(μ1)(2R)1fl=(1.71)(212.5)fl=12514 cmEffectivefocallengthofcombinationis1Feff=1fl+1fg1+1fg2=+22514125Feff=1254=31.25 cm

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