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Question

A thin convergent glass lens (μg=1.5) has a power of +5.0D. When this lens is immersed in a liquid of refractive index μl, it acts as a divergent lens of focal length 100cm. The value of μl is?

A
1.37
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B
3
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C
5.2
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D
2.2
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Solution

The correct option is A 1.37
Formula for focal length is:
1f=(μ2μ11)(1R11R2)
Here, 1f=+5D,μ2=1.5,μ1=1
Then,
+5=(0.5)(1R11R2)(i)f=100cm=1mμ2=1.5
Let μ1=x.
11=(1.5x1)(1R11R2)1=(1.5x1)(1R11R2)(ii)
Dividing (i) by (ii),
5=0.5(1.5x1)7.5x5=0.5x=1.37

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