A beaker of radius $r$ is filled with water (refractive index $\frac{4}{3}$ ) up to a height $H$ as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is $h(h \ll H, h \ll r)$, as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature $R$. Which of the following is/are correct? (g is the acceleration due to gravity)