Absolute refractive index of a medium is 'X'. Refractive index of same medium w.r.t. to air is 'Y' and absolute refractive index of air is 'Z'. Then, the relation between them is

The refractive index of one medium with respect to another is given by:

    μ₂₁ = μ₂ / μ₁

Here:

• μ₂₁ is the refractive index of medium 2 with respect to medium 1.
• μ₂ and μ₁ are the absolute refractive indexes of medium 2 and medium 1, respectively.

In this case:

• The absolute refractive index of the medium is X.
• The refractive index of the same medium with respect to air is Y.
• The absolute refractive index of air is Z.

The relationship can be written as:

    Y = X / Z

Final Relationship

Rearranging the above equation:

    X = Y × Z

This shows that the absolute refractive index of the medium (X) is the product of the refractive index of the medium with respect to air (Y) and the absolute refractive index of air (Z).

Conclusion

The relationship between the refractive indexes is summarized as:

    X = Y × Z
    Y = X / Z
    Z = X / Y

This analysis highlights the significance of the absolute refractive index in understanding the optical properties of different media.