A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be the pole of the mirror and C it's centre of curvature. A point object is placed at C. It has a real image, also located at C (a condition called auto-collimation). If the mirror is now filled with water, the image will be:

Two mirrors are inclined at an angle $\theta$, as shown in the figure. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after the third reflection, if

Two plane mirrors, $\mathrm{A}$ and $\mathrm{B}$, are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$, at a point just inside one end of $\mathrm{A}$. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
  

How much water should be filled in a container $21 \mathrm{cm}$ in height, so that it appears half filled when viewed from the top of the container?

[given that, ${}_a\mu _w=\frac{4}{3}$]