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# Absolute Refractive Index of a medium is $X$ refractive index of same medium with respect to air is $Y$ and absolute refractive index of air is $Z$ . Then the relation between them is:(A) $X = \dfrac{Y}{Z}$ (B) $Y = \dfrac{X}{Z}$ (C) $Z = \dfrac{Y}{X}$ (D) $Y = \dfrac{1}{{XZ}}$

Last updated date: 16th Jun 2024
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Hint: Relative refractive index of a medium with respect to another medium is defined as the ratio of their absolute refractive indices. Relative refractive index of medium with respect to air is given by the ratio of absolute refractive index of medium and the absolute refractive index of air.

Complete Step by Step Solution
The absolute refractive index is defined as the ratio of the speed of light in vacuum and in the given medium. The absolute refractive index should never be less than 1.
It has been given that,
The absolute refractive index of a medium = $X$
The absolute refractive index of air = $Z$
Refractive index of medium with respect to air is $Y$ .
To understand the relation between them, it is now necessary to define the relative refractive index.
The ratio of the speed of light in a vacuum to the speed of monochromatic light in the substance of interest. Also called the absolute index of refraction it is commonly called the refractive index or index of refraction. However, those two terms are also sometimes applied without warning to the ration found when the ray emerges into the air instead of a vacuum. That ratio should be called a relative refractive index.
The ratio of the first value to the second one is about the relative refractive index of the glass. In the case of a concave surface, beams originally propagating along the main optical axis will be refracted in such a way that they will never intersect.
So, Relative refractive index of medium with respect to air is given by the ratio of absolute refractive index of medium and the absolute refractive index of air.
Thus, ${\text{Relative refractive index of medium = }}\dfrac{{{\text{absolute refractive index of medium}}}}{{{\text{absolute refractive index of air}}}}$
Assigning the values stated in the question we get,
$= {X \mathord{\left/ {\vphantom {X Z}} \right.} Z}$
According to the question,
Relative refractive index of medium with respect to air = $Y$ .
So, the relation between them is $Y = \dfrac{X}{Z}$ .

Note
The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, $c\; = \;299792458\;m{s^{ - 1}}$ , and the phase velocity v of light in the medium,
The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves.
The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Historically air at a standardized pressure and temperature has been common as a reference medium.
According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. For visible light most transparent media have refractive indices between 1 and 2.