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Q.

The refractive index of water is $1.33$ , and the speed of light in air is $3 \times 10^{8} m / s$ . Calculate the speed of light in water.

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a

2.25 \times 10^{8} m / s

b

1.33 \times 10^{8} m / s

c

2 \times 10^{8} m / s

d

2.75 \times 10^{8} m / s

answer is A.

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Detailed Solution

The speed of light in water is

2.25 \times 10^{8} m / s

.
The refractive index of any material with respect to air or vacuum is called the absolute refractive index. The absolute refractive index (n) of any material is the ratio of the speed of light in a vacuum to the speed of light in that particular medium.

n = \frac{c}{v}

where n = absolute refractive index of the medium
c = speed of light in vacuum
v = speed of light in that medium

1.33 = \frac{3 \times 10^{8}}{v}

\Rightarrow v = \frac{3 \times 10^{8}}{1.33}

\Rightarrow v = 2.25 \times 10^{8} m / s

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