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Absolute refractive indices of the media A and B are $2$ and $1.5$ respectively. If the speed of light in medium B is $2 \times 10^{8} m / s$ , calculate the speed of light in medium A.

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3 \times 10^{8} m / s

2 \times 10^{8} m / s

1.5 \times 10^{8} m / s

2.5 \times 10^{8} m / s

answer is C.

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Detailed Solution

Given, absolute refractive index of medium

A = R_{1} = 2

Absolute refractive index of medium

B = R_{2} = 1.5

Speed of light in medium

B = 2 \times 10^{8} m / s

We know that,

R_{2} = \frac{speed of light in vacuum}{speed of light in medium B}

R_{2} = 1.5

Speed of light in vacuum

= 1.5 \times

Speed of light in medium

B

\Rightarrow

= 1.5 \times 2 \times 10^{8} m / s

\Rightarrow

= 3 {\times 10}^{8} m / s

Also,

R_{1} = \frac{speed of light in vacuum}{speed of light in medium A}

R_{1} = 2

Speed of light in medium

A = \frac{(Speed of light in vacuum)}{2}

\Rightarrow

= \frac{3 {\times 10}^{8}}{2} \times 10^{8} m / s

= 1.5 \times 10^{8} m / s

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