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State the law of refraction of light which defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air. The refractive indices of glass and water with respect to vacuum are 3/2 and 4/3 respectively.If the speed of light in glass is 2 × 108 m/s, find the speed of light ini. vacuumii. water
The law of refraction that defines the refractive index of a medium with respect to the other is given by the first law of refraction known as Snell’s law.
First law of refraction:
It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This is known as Snell’s law.
Mathematically, it can be given as follows:
$\frac{sin\ i}{sin\ r} =constant=^a\mu_{b}$.
Here, $^a\mu_{b}$ is the relative refractive index of medium $b$ with respect to medium $a$.
Consider a ray of light travelling from medium $B$ into medium $A$. Let $v_1$ be the speed of light in medium $A$ and $v_2$ be the speed of light in medium $B$. Then, the refractive index of medium $A$ with respect to medium $B$ is given by:
$n_{AB} =\frac{v_{2}}{v_{1}}$
If one medium is vacuum or air then the constant is known as the absolute refractive index of the medium.
Let, absolute refractive index of glass, $n_{g} =\frac{3}{2}$
Absolute refractive index of water, $n_{w} =\frac{4}{3}$
Speed of light in glass, $v_{g} =2\times 10^{8} \ m/s$
(i) Speed of light in vacuum, $n_{g} =\frac{c}{n_{g}}$
$c=n_{g} \times v_{g}$
$c=\frac{3}{2} \times 2\times 10^{8} \ m/s$
$c=3\times 10^{8} \ m/s$
(ii) Speed of light in water, $n_{w} =\frac{c}{v_{w}}$
$v_{w} =\frac{c}{n_{w}}$
$v_{w} =\frac{3\times 10^{8} \ m/s}{\frac{4}{3}}$
$v_{w} =2.25\times 10^{8} \ m/s$
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