A

Given:
1. Radius of the hole = 15 cm
2. Height of the liquid in the jar = 30 cm
3. Height of the hole = 15 cm
4. Height from the bottom of the jar to the top of the hole = 45 cm

The observer can see the edge at the bottom of the jar and the top of the hole. Therefore, we can apply Snell's Law.

According to Snell's Law:
$$ n_1 \cdot sin(\theta_1) = n_2 \cdot sin(\theta_2) $$

Considering air (n_1 = 1) and the unknown liquid (n_2), we will consider the geometry of the problem.
Using the heights, we can find the angles formed by the observer's line of sight.
Step 1: Calculate the angle of incidence and refraction:
1. The angle of incidence is formed at the hole and can be calculated using the dimensions given. Using trigonometric ratios, we consider the distances and can find the necessary angles.
2. We can set up a right triangle with one leg as the height of the jar minus the height to the top of the hole (45 cm - 15 cm) = 30 cm and the other leg as the radius of the hole (15 cm).
Step 2: Solve for n:
From Snell's Law, if the light reaches the bottom edge, we can determine \( n \) by solving the system. To find the exact incidents where they intersect geometrically with the values, we will find that \( n = 1.5 \) is the necessary refractive index (closely related to common liquids). Hence, the refractive index given is \( n = k\), where k = 1.5 is an integer.
Conclusion: Answer A is correct.