A light ray enters from medium A to medium B as shown in the figure.
Generated by claude-sonnet-4-6 · 2026-06-15 06:52 · grounding rag
Model Answer
(a) Medium A is denser. Since the refracted ray in medium B bends away from the normal, the ray is moving from a denser medium to a rarer medium. A ray travelling from a denser medium to a rarer medium speeds up and bends away from the normal.
(b) Refractive index of B with respect to A:
$$n_{BA} = \frac{\text{Speed of light in medium A}}{\text{Speed of light in medium B}} = \frac{v_a}{v_b}$$
Source: Chapter 9, Section 9.3.2 — The Refractive Index
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Explanation
- Part (a): The key rule is: denser → rarer = bends away from normal; rarer → denser = bends toward normal. Since the ray bends away from normal in B, A must be the denser medium. Always justify using this rule.
- Part (b): Use formula $n_{21} = v_1/v_2$ from Eq. 9.5 — refractive index of medium 2 w.r.t. medium 1 = speed in medium 1 ÷ speed in medium 2. Here medium 1 = A, medium 2 = B, so $n_{BA} = v_a/v_b$.