A pond of depth `20 cm` is half filled with an oil of `mu = 1.4` and the other half is filled with water of refractive index `1.33`. Calculate apparent depth of the tank when viewed normally.

Answer

To solve the problem of finding the apparent depth of a pond that is half-filled with oil and half-filled with water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Depths and Refractive Indices**:
- The total depth of the pond is 20 cm.
- The pond is half-filled with oil (10 cm) and half-filled with water (10 cm).
- The refractive index of oil (μ_oil) = 1.4.
- The refractive index of water (μ_water) = 1.33.

2. **Calculate the Apparent Depth in Oil**:
- The formula for apparent depth when viewed from above is given by:
\[ \text{Apparent Depth} = \frac{D}{\mu} \]
- For the oil layer (10 cm):
\[ \text{Apparent Depth}_{oil} = \frac{10 \text{ cm}}{1.4} = 7.14 \text{ cm} \]

3. **Calculate the Apparent Depth in Water**:
- For the water layer (10 cm):
\[ \text{Apparent Depth}_{water} = \frac{10 \text{ cm}}{1.33} \approx 7.52 \text{ cm} \]

4. **Total Apparent Depth**:
- The total apparent depth of the pond is the sum of the apparent depths of both layers:
\[ \text{Total Apparent Depth} = \text{Apparent Depth}_{oil} + \text{Apparent Depth}_{water} \]
- Substituting the values:
\[ \text{Total Apparent Depth} = 7.14 \text{ cm} + 7.52 \text{ cm} \approx 14.66 \text{ cm} \]

5. **Final Answer**:
- The apparent depth of the tank when viewed normally is approximately **14.66 cm**.