Ray Optics

JEE Main level, single correct, medium

103 of 295

Question 103 of 295

The difference of speed of light in the two media AA and B(vA−vB)B\left({v}_{A}-{v}_{B}\right) is 2.6×107ms−12.6\times {10}^{7}m{s}^{-1}. If the refractive index of medium BB is 1.471.47, then the ratio of refractive index of medium BB to medium AA is: (Given : speed of light in vacuum c=3×108ms−1c=3\times {10}^{8}{ms}^{-1})

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Answer: (C) 1.131.13

The speed of light in the medium BB will be, vB=cμB{v}_{B}=\dfrac{c}{{\mu }_{B}}
The speed of light in the medium
AA will be, vA=cμA{v}_{A}=\dfrac{c}{{\mu }_{A}}.
Now,

vA−vB=c(1μA−1μB)⇒2.6×107=3×108×(1μA−11.47)⇒μA=1.13{v}_{A}-{v}_{B}=c\left(\dfrac{1}{{\mu }_{A}}-\dfrac{1}{{\mu }_{B}}\right) \Rightarrow 2.6\times {10}^{7}=3\times {10}^{8}\times \left(\dfrac{1}{{\mu }_{A}}-\dfrac{1}{1.47}\right) \Rightarrow {\mu }_{A}=1.13

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