Science (086) — AI-generated practice question

(i) Explanation with Ray Diagram:

When light rays from the coin travel from water (denser medium) to air (rarer medium), they bend away from the normal at the water-air interface. Our eyes trace these refracted rays back in straight lines, and they appear to meet at a point higher than the actual position of the coin. Thus, the coin appears raised/closer to the surface.

Ray Diagram:

```
Air | / ← Refracted ray (bends away from normal)
--------|/------- water surface
Water |\
| \ ← Actual ray from coin
| [COIN] (actual position)
(apparent position shown higher up)
```

(ii) Calculation of Apparent Depth:

$$\text{Refractive index} = \frac{\text{Real depth}}{\text{Apparent depth}}$$

$$\text{Apparent depth} = \frac{\text{Real depth}}{n} = \frac{40}{1.33} \approx 30.08 \text{ cm}$$

Apparent depth ≈ 30.1 cm

(iii) Effect of higher refractive index (n = 1.5):

$$\text{Apparent depth} = \frac{40}{1.5} \approx 26.67 \text{ cm}$$

The apparent depth decreases further (from 30.1 cm to 26.7 cm).

Conclusion: Higher the refractive index of the medium, lesser the apparent depth — i.e., apparent depth is inversely proportional to refractive index.

Source: Chapter 9, Section 9.3 – Refraction of Light; Section 9.3.2 – The Refractive Index

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• Part (i): Examiners expect the key phrase "bends away from normal" (denser to rarer) and the idea that the eye traces rays backward. A simple diagram showing the coin, two diverging refracted rays, and the apparent (virtual) position earns full credit.
• Part (ii): The formula n = Real depth / Apparent depth is standard and must be recalled. Show substitution clearly.
• Part (iii): Always compare the two values numerically, then state the inverse relationship explicitly — examiners look for both the calculation and the conclusion.