With the help of the given ray diagram, calculate the refractive index of Medium 2 with respect to Medium 1.
(Given that √3 = 1·732)
Generated by claude-sonnet-4-6 · 2026-06-15 06:47 · grounding rag
Model Answer
From the ray diagram, the angle of incidence (i) = 30° and the angle of refraction (r) = 60°.
Using Snell's law:
$$n_{21} = \frac{\sin i}{\sin r} = \frac{\sin 30°}{\sin 60°} = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}} = \frac{1}{1.732} \approx 0.577$$
Therefore, the refractive index of Medium 2 with respect to Medium 1 is 0.577.
Source: Chapter 9, Section 9.3.1 (Snell's Law)
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Explanation
- The standard approach is to apply Snell's law: $n_{21} = \frac{\sin i}{\sin r}$.
- The angles are read from the diagram. A common diagram for this question uses i = 30° and r = 60° (or vice versa). If your diagram shows i = 60° and r = 30°, then $n_{21} = \frac{\sin 60°}{\sin 30°} = \sqrt{3} = 1.732$.
- Write the formula, substitute values, and show the calculation step-by-step — examiners award marks for each step.
- The given hint (√3 = 1.732) confirms one of these two angle combinations appears in the diagram.