Science (086) — CBSE Class 10 board question

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

---

• 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 $9/4 > 2$.