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Question

Two identical glass (μg=3/2) equiconvex lenses of focal length f are kept in contact. The space between the two lenses is filled with water (μw=4/3). The focal length of the combination is

A
f
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B
f2
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C
4f3
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D
3f4
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Solution

The correct option is D 3f4
Water in between the lenses can be considered to be a concave lens with the refractive index of water as shown in the figure. This suggests that the radius of curvature of all the lenses is same.

For the convex lenses,
1f=(μg1)2R=(321)2R

Hence, R=f

For the concave lens,

1f=(μwater1)(2R)=23f

Power of the lenses get added,
1fcombination=1f+1f+1f
1fcombination=1f+23f+1f

Hence, fcombination=3f4


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