Science (086) — CBSE Class 10 board question

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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• 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.