A

To find the apparent depth of the non-homogeneous liquid, we start from the definition of apparent depth in terms of refractive index. Given that the refractive index varies with 'y', we can use the average refractive index for the liquid over the depth 'H'. The apparent depth 'd' can be expressed as:
$$ d = \frac{H}{\mu_{avg}} $$
Where:

• \mu_{avg} is the average refractive index. We obtain it by integrating \mu(y) over the depth 'H'.

Using the provided refractive index function and calculating the average value across the depth gives us the exact numerical value of the apparent depth. Therefore, the calculated value for the apparent depth is option A.