The refractive index of medium A with respect to medium B is 2/3, and the refractive index of medium B with respect to air is 1.5. Which medium — A, B, or air — has (i) the highest optical density and (ii) the lowest optical density? Justify your answer.
Generated by claude-sonnet-4-6 · 2026-06-26 01:12 · grounding rag
Model Answer
Given:
$n_{AB} = \frac{2}{3}$, $n_{B,\text{air}} = 1.5$
Finding absolute refractive index of A:
$$n_{B,\text{air}} = 1.5 \Rightarrow n_B = 1.5$$
$$n_{AB} = \frac{n_A}{n_B} = \frac{2}{3} \Rightarrow n_A = \frac{2}{3} \times 1.5 = 1.0$$
Summary of refractive indices:
- Air ≈ 1.0
- Medium A = 1.0
- Medium B = 1.5
(i) Highest optical density: Medium B, as it has the highest refractive index (1.5). A higher refractive index means greater optical density.
(ii) Lowest optical density: Air (and Medium A), both have refractive index ≈ 1.0, making them equally and least optically dense.
Source: Chapter 9, Section 9.3.2
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Explanation
- The key formula used is $n_{AB} = \dfrac{n_A}{n_B}$, which lets you find the absolute refractive index of A.
- Examiners expect you to show the calculation of $n_A$ clearly.
- Optical density is directly proportional to refractive index — higher refractive index = optically denser medium (as stated in the "More to Know" box).
- Note: optical density ≠ mass density. Don't confuse the two.
- If $n_A = 1.0$ exactly equals air, full credit is given for naming both as lowest; mentioning Medium A alone is also acceptable.