Step 1: Understanding the Question:
The problem asks for the apparent depth of a container filled with multiple layers of different liquids. The observer is looking from above (usually air).
Step 2: Key Formula or Approach:
The total apparent depth for multiple layers is the sum of the apparent depths of individual layers:
\[ d_{\text{app}} = \sum \frac{d_{i}}{\mu_{i}} = \frac{d_{1}}{\mu_{1}} + \frac{d_{2}}{\mu_{2}} + \frac{d_{3}}{\mu_{3}} \]
Step 3: Detailed Explanation:
Given:
Layer 1: \(d_{1} = 3 \text{ cm}\), \(\mu_{1} = 3/2\)
Layer 2: \(d_{2} = 4 \text{ cm}\), \(\mu_{2} = 4/3\)
Layer 3: \(d_{3} = 6 \text{ cm}\), \(\mu_{3} = 6/5\)
Total apparent depth:
\[ d_{\text{app}} = \frac{3}{3/2} + \frac{4}{4/3} + \frac{6}{6/5} \]
\[ d_{\text{app}} = \left( 3 \times \frac{2}{3} \right) + \left( 4 \times \frac{3}{4} \right) + \left( 6 \times \frac{5}{6} \right) \]
\[ d_{\text{app}} = 2 + 3 + 5 = 10 \text{ cm} \]
Step 4: Final Answer:
The apparent depth of the vessel is \(10 \text{ cm}\).