A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt { 7 } \mathrm {~m}$. The refractive index of water is $\frac { 4 } { 3 }$. The area of the surface of water through which light from the bulb can emerge out is $x \pi \mathrm {~m} ^ { 2 }$. The value of $x$ is $\_\_\_\_$.