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Refractive Index of four mediums $A, B, C$ and $D$ are $1.31, 1.65, 1.44$ and $1.50$ respectively. The velocity of light is maximum in
A) Medium $B$
B) Medium $D$
C) Medium $C$
D) Medium $A$

Last updated date: 23rd May 2024
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Hint: The refractive index is the ratio of the velocity of light in the vacuum (or air) to the velocity of light in the translucent substance. It bends when light travels through the interface between two mediums with different refractive indices. This property is very useful in the design with optical lenses as it helps the bending angle of the light beam to be measured when travelling from one translucent medium to another.

Complete step by step answer:
In a typical material system consisting of a waveguide structure with a core active EO polymer and passive polymer as top and bottom cladding, refractive index is significant. The refractive indices of each layer of the stack must be closely balanced to ensure the maximum overlap between the light mode and the active EO layer in order to construct an appropriate waveguide to optimise the interaction between light and the chromosphere.
If $i$ is the angle of incidence of the vacuum ray (angle between the incoming ray and the angle perpendicular to the medium’s surface, called normal) and r is the angle of refraction (angle between the medium's ray and the normal), the refractive index n is defined as the ratio of the sine to the angle of refraction, i.e. $n = \dfrac{{\sin i}} {{\sin r}} $. The refractive index is also proportional to the light velocity $c$ of the given empty space wavelength, divided by its velocity $v$ in the material, or $n = \dfrac{c}{v}$.
Since refractive index is inversely proportional to velocity of light in the medium, therefore, the medium having the least refractive index will have highest velocity.

Therefore, the correct answer is option D.

Note: In quality control and in the identification of various materials which are transparent or translucent to the ray of light, refractive indices could also be used. The refractive index of the x-rays is just under one, so that, unlike a light ray, an X-ray that is inputting a fragment of glass from the air is bending away from nature. In this case, the equation $n = \dfrac{c}{v}$ correctly shows that the X-ray velocity in glass and other materials is greater than its velocity in empty space.