An object is initially at a distance of $100 \mathrm{cm}$  from a plane mirror. If the mirror approaches the object at a speed of $5 \mathrm{cm} {\mathrm{s}}^{-1}$ then after $6 \mathrm{s}$, the distance between the object and its image will be

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

White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray air contains.

A rod of glass $(\mu =1.5)$ and of the square cross-section is bent into the shape as shown in the figure. A parallel beam of light falls on the plane flat surface $A$ as shown in the figure. If $d$ is the width of a side and $R$ is the radius of a circular arc, then for what maximum value of $\frac{\mathit{d}}{\mathit{R}}$ light entering the glass slab through surface $A$ emerges from the glass through $B$?