(a) Define absolute refractive index of an optical medium.

(b) Table: Material Medium / Refractive Index — A: 1.50, B: 1.46, C: 1.31, D: 1.77.

Arrange these material mediums given in the table in increasing order of speed of light through them.

(a) As stated in the chapter (Section 9.3.2), 'If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium... $n_m = \dfrac{\text{Speed of light in air}}{\text{Speed of light in the medium}} = \dfrac{c}{v}$' (Eq. 9.7).

(b) From Eq. 9.7, $n_m = c/v \Rightarrow v = \dfrac{c}{n_m}$. Since $c$ is constant, the speed of light in a medium is inversely proportional to its refractive index — the higher the refractive index, the slower the light travels (the chapter notes: 'The speed of light is higher in a rarer medium than a denser medium').

Given refractive indices: A $=1.50$, B $=1.46$, C $=1.31$, D $=1.77$. These match Table 9.3 of the chapter: Benzene $=1.50$ (A), Fused quartz $=1.46$ (B), Ice $=1.31$ (C), Sapphire $=1.77$ (D).

Arranging refractive index in decreasing order gives the speed in increasing order:

$$n_D(1.77) > n_A(1.50) > n_B(1.46) > n_C(1.31)$$

$$\Rightarrow v_D < v_A < v_B < v_C$$

So the mediums in increasing order of speed of light through them are: D, A, B, C — i.e. light travels slowest through medium D (most optically dense, $n=1.77$, matching sapphire in Table 9.3) and fastest through medium C (least optically dense of the four, $n=1.31$, matching ice in Table 9.3).