Absolute refractive index of glass and water is 3/2 and 4/3 respectively. If the speed of light in glass is 2 × 10⁸ m/s, the speed of light in water is :
Generated by claude-sonnet-4-6 · 2026-06-15 06:49 · grounding rag
Model Answer
Answer: (A) 9/4 × 10⁸ m/s
Using $n = \frac{c}{v}$: Speed of light in water = $\frac{n_g \times v_g}{n_w} = \frac{\frac{3}{2} \times 2 \times 10^8}{\frac{4}{3}} = \frac{3 \times 10^8}{\frac{4}{3}} = \frac{9}{4} \times 10^8$ m/s.
Source: Chapter 9, Section 9.3.2
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Explanation
- Use $n = c/v$, so $v = c/n$. Since $n_g \cdot v_g = n_w \cdot v_w = c$ (constant), you can write $v_w = \frac{n_g \times v_g}{n_w}$.
- Substituting: $v_w = \frac{(3/2) \times 2 \times 10^8}{4/3} = \frac{3 \times 10^8}{4/3} = \frac{9}{4} \times 10^8$ m/s.
- Key concept: higher refractive index → lower speed of light in that medium. Water ($n = 4/3$) is rarer than glass ($n = 3/2$), so light travels faster in water — which checks out since $9/4 > 2$.