A water pond appears to be `2*7m` dep. If the refractive index of water is `4//3`, find the actual depth of the pond.

Answer

To find the actual depth of the pond, we can use the relationship between the apparent depth, actual depth, and the refractive index of the medium. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Apparent depth (DA) = 2.7 m
- Refractive index (n) = 4/3

### Step 2: Write the formula for refractive index
The refractive index (n) is defined as the ratio of the actual depth (D) to the apparent depth (DA):
\[ n = \frac{D}{DA} \]

### Step 3: Rearrange the formula to find actual depth
From the formula, we can rearrange it to solve for the actual depth (D):
\[ D = n \times DA \]

### Step 4: Substitute the known values into the formula
Now, substitute the values of n and DA into the equation:
\[ D = \left(\frac{4}{3}\right) \times 2.7 \]

### Step 5: Calculate the actual depth
Now, perform the multiplication:
\[ D = \frac{4 \times 2.7}{3} \]
\[ D = \frac{10.8}{3} \]
\[ D = 3.6 \, \text{m} \]

### Conclusion
The actual depth of the pond is 3.6 meters.

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