The absolute refractive index of diamond is 2.42. What does this mean physically? If the speed of light in air is 3 × 10⁸ m s⁻¹, calculate the speed of light in diamond.
Generated by claude-sonnet-4-6 · 2026-06-26 01:12 · grounding rag
Model Answer
Physical meaning: The absolute refractive index of diamond is 2.42 means that the speed of light in air is 2.42 times the speed of light in diamond (i.e., light travels 2.42 times faster in air than in diamond).
Calculation:
$$n = \frac{c}{v} \Rightarrow v = \frac{c}{n} = \frac{3 \times 10^8}{2.42}$$
$$v = 1.24 \times 10^8 \text{ m s}^{-1}$$
The speed of light in diamond is $1.24 \times 10^8$ m s⁻¹.
Source: Chapter 9, Section 9.3.2 – The Refractive Index
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Explanation
- For the meaning part (1 mark): state clearly that the refractive index is the ratio of speed of light in air to speed in the medium. Saying "light slows down by a factor of 2.42 in diamond" earns the mark.
- For the calculation part (1 mark): use $n = c/v$, substitute correctly, and show the final answer with units. Division: $3 \times 10^8 \div 2.42 \approx 1.24 \times 10^8$ m s⁻¹.
- Do not just write the formula without substituting values — examiners expect full working for numericals.