If the refractive index of a medium is $1.25$ , find the speed of light in this medium. Given the speed of light in air is $3 \times 10^{8} m / s$ .

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Solution

Step 1: Given data
$R e f r a c t i v e i n d e x o f a m e d i u m = 1.25$
$S p e e d o f l i g h t i n a i r = 3 \times 10^{8} m / s$
Step 2: Formula used
$R e f r a c t i v e i n d e x o f a m e d i u m = \frac{s p e e d o f l i g h t i n a i r}{s p e e d o f l i g h t i n a g i v e n m e d i u m}$
Step 3: Calculating the speed of light
$R e f r a c t i v e i n d e x o f a m e d i u m = \frac{s p e e d o f l i g h t i n a i r}{s p e e d o f l i g h t i n a g i v e n m e d i u m}$
$1.25 = \frac{3 \times 10^{8} m / s}{s p e e d o f l i g h t i n a g i v e n m e d i u m}$
$∴ s p e e d o f l i g h t i n a g i v e n m e d i u m = \frac{3 \times 10^{8} m / s}{1.25}$
$= 2.4 \times 10^{8} m / s$
Hence, the speed of light in a given medium is $2.4 \times 10^{8} m / s$ .

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(1) The speed of light in a transparent medium is 2.4 × 10⁸ m/s. Calculate absolute refractive index of the medium.

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(3) Refractive index of water is 4/3 and speed of light in air is 3×10⁸ m/s. Find speed of light in water.

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