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The speed of light in substance $X$ is $1.25\times {10^8m/s}$ and that in air is $3\times {10^8m/s}$. The refractive index of this substance will be:(a) 2.4 (b) 0.4 (c) 4.2 (d) 3.75
(a) 2.4
Explanation
Given:
Speed of light in substance X = $1.25\times {10^8m/s}$
Speed of light in air= $3.0\times {10^8}m/s$
To find: Refractive index of the substance X.
Solution:
From the formula for refractive index, we know that-
$Refractive\ index\ of\ a\ medium=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ medium}$
For substance X:
$Refractive\ index\ of\ substance\ X=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ substamce\ X}$
Substituting the given value, we get-
$Refractive\ index\ of\ substance\ X=\frac {3.0\times {10^8}m/s}{1.25\times {10^8m/s}}$
$Refractive\ index\ of\ substance\ X=2.4$
Thus, the refractive index of substance X is 2.4.
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