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Question

The refractive index and the permeability of a medium are 1.5Hm-1 and 5×10-7Hm-1 respectively. The relative permittivity of the medium is nearly


A

25

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B

15

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C

81

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D

10

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E

6

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Solution

The correct option is E

6


Step 1: Given data

Refractive indexn=1.5Hm-1

Permeability of a medium=5×10-7Hm-1

Step 2: Formula used

The refractive index of the medium is given by,

n=cvwhere, n=refractive index, c=speed of light, and v=speed of light in vacuum

Step 3: Compute the speed

Substitute the known values in the formula n=cv

1·5=3·0×108vv=3·0×1081·5v=2·0×108ms

Step 4: Compute the relative permittivity

It is understood that ,v=1με=1μεεr

where μ=Permeability of a medium, εr=relative permeability of the medium, ε0=permeability of the medium.

Substitute the known values in the formula,

v=1με=1μεεr1με=1μεεr2·0×108=15×10-7×εr×8·85×10-12εr=12·0×1082×5×10-7×8·85×10-12εr6

Thus, the relative permittivity of the medium is 6.

Hence, option E is the correct answer.


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