Question

(a) State the laws of refraction of light. Explain the term absolute refractive index of a medium and write an expression to relate it with the speed of light in vacuum.
(b) The absolute refractive indices of two media 'A' and 'B' are 2.0 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:
(i) vacuum,
(ii) medium 'A'.

Answer 1

(a) Laws of Refraction:
(1) ​The incident ray, the refracted ray and the normal to the interface of two media at the point of incidence all lie in the same plane.
(2) For the light of a given color and for given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This is also known as Snell's Law.
Mathematically, it can be given as follows:
$\frac{sini}{sinr}=constant=A_{{\mu }_B}$
Here, $A_{{\mu }_B}$ is the relative refractive index of medium B with respect to medium A.
The absolute refractive index is the value of refractive index of a medium with respect to the vacuum.
${\mu }_B=\frac{c}{v}$
Where
c = Speed of light in vacuum
v = Speed of light in medium B
Here, ${\mu }_B$ is the absolute refractive index of medium
(b) Absolute refractive index of medium 'A',${\mu }_A=2.0$
Absolute refractive index of medium 'B', ${\mu }_B=2.0$
(i) For medium 'B',
$1.5=\frac{c}{(2\times {10}^8)}$
$\Rightarrow c=2\times {10}^8\times 1.5$
$\Rightarrow c=3\times {10}^8$
Speed of light in vacuum is $c=3\times {10}^{8}m{s}^{-1}$
(ii) For medium 'A',
${\mu }_A=\frac{c}{v}$
$\Rightarrow v=\frac{c}{{\mu }_A}$
$v=\frac{3\times {10}^8}{2}$
$v=1.5\times {10}^8$
Thus, speed of light in medium 'A' is $1.5\times {10}^{8}m{s}^{-1}$