Introduction:
Young's double-slit experiment is a classic experiment that demonstrates the wave nature of light. It involves passing light through two closely spaced slits and observing the resulting interference pattern on a screen. The position of the bright fringes (maxima) in the interference pattern can be determined using the formula:

y = mλL/d

where y is the y-coordinate of the fringe, m is the order of the fringe, λ is the wavelength of light, L is the distance from the slits to the screen, and d is the distance between the slits.

Given Information:
- y-coordinate of the central maximum (m=0) = 2 cm
- y-coordinate of the 10th maximum (m=10) = 5 cm

Calculating wavelength of light:
Using the formula, we can calculate the wavelength of light used in the experiment. Since the central maximum is at m=0, the equation simplifies to:

2 cm = 0 * λ * L / d

Since the order of the fringe is zero, the y-coordinate is also zero. This means the distance between the slits (d) is much larger than the distance to the screen (L). Therefore, we can assume that the light rays are parallel, and the distance between the slits does not affect the central maximum position. So, we have:

2 cm = 0 * λ * L

Since 0 multiplied by any value is zero, we get:

2 cm = 0

This equation tells us that the wavelength of light used in the experiment is zero, which is not possible. Therefore, there seems to be an error in the given information.

Impact of refractive index:
The refractive index of a medium affects the propagation of light through it. When the Young's double-slit experiment apparatus is immersed in a liquid with a refractive index of 1.5, the speed of light changes as it enters the liquid. This change in speed can affect the interference pattern observed on the screen.

Conclusion:
Without the correct wavelength information, it is not possible to accurately calculate the corresponding y-coordinate when the YDSE apparatus is immersed in a liquid with a refractive index of 1.5. It is important to have accurate and complete information to perform calculations and analyze the effects of different parameters in an experiment.