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 calculating the apparent depth of a pond that is half filled with oil and half filled with water, we can follow these steps:

### Step 1: Understand the setup
The pond has a total depth of 20 cm, with the upper half (10 cm) filled with oil (refractive index \( \mu_{oil} = 1.4 \)) and the lower half (10 cm) filled with water (refractive index \( \mu_{water} = 1.33 \)).

### Step 2: Calculate the apparent depth for the water layer
The formula for apparent depth \( S' \) when viewed normally is given by:
\[ S' = \frac{H}{\mu} \]
where \( H \) is the actual depth and \( \mu \) is the refractive index.

For the water layer:
- Actual depth \( H_{water} = 10 \, \text{cm} \)
- Refractive index \( \mu_{water} = 1.33 \)

Using the formula:
\[ S'_{water} = \frac{10 \, \text{cm}}{1.33} \approx 7.52 \, \text{cm} \]

### Step 3: Calculate the apparent depth for the oil layer
Now, we apply the same formula for the oil layer:
- Actual depth \( H_{oil} = 10 \, \text{cm} \)
- Refractive index \( \mu_{oil} = 1.4 \)

Using the formula:
\[ S'_{oil} = \frac{10 \, \text{cm}}{1.4} \approx 7.14 \, \text{cm} \]

### Step 4: Calculate the total apparent depth
The total apparent depth \( S'_{total} \) is the sum of the apparent depths of both layers:
\[ S'_{total} = S'_{water} + S'_{oil} = 7.52 \, \text{cm} + 7.14 \, \text{cm} \approx 14.66 \, \text{cm} \]

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

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