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Question

The focal length of a plano convex lens is 'f' and its refractive index is 1.5. It is kept over a plane glass plate with its curved surface touching the glass plate. The gap between the lens and the glass plate is filled by a liquid. As a result, the effective focal length of the combination becomes 2f. Then the refractive index of the liquid is

A
1.25
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B
1.33
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C
1.5
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D
2
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Solution

The correct option is A 1.25

From lens maker's formula:-

1f=(μ1)(1R11R2)

For, plano-convex lens:-

1f=(1.51)(11R)=12R

f=2R

Now, we can treat the fluid below the plano-convex lens as a plano -concave lens of refractive index μ and focal length f

So, 1f=(μ1)(1R1)

1f=1μR

Now, for combination:-

1F=1f+1f

12f=1f+1μR

1μR=12f=14R

1μ=0.25

μ=1.25

Answer-(A)

831054_598568_ans_232a508f51604c0e878bddef12730605.jpg

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