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A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, the light takes 8.72 ns to travel the length of the tube, but when the tube is filled with a transparent jelly, the light takes 1.82 ns longer to travel its length. What is the refractive index of this jelly?

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Answer:

1.208

Explanation:

L = Length of tube

c = Speed of light in air

v = Speed of light in jelly

Time taken by light in tube

[tex]\dfrac{L}{c}=8.72[/tex]

Time taken when jelly is present

[tex]\dfrac{L}{v}=8.72+1.82\\\Rightarrow \dfrac{L}{v}=10.54\ ns[/tex]

Dividing the above equations we get

[tex]\dfrac{v}{c}=\dfrac{8.72}{10.54}\\\Rightarrow \dfrac{c}{v}=\dfrac{10.54}{8.72}\\\Rightarrow n=1.208[/tex]

The refractive index of the jelly is 1.208

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