In the mid-19th century, French physicist Foucault made the most accurate measurement of the speed of light using a laboratory-sized apparatus consisting of rotating and fixed mirrors. Consider a source of light emitting a beam which bounces off a rotating mirror and then reflects off a small fixed mirror. By the time it reaches back to the rotating mirror, the mirror has rotated by a small angle. This rotation will deflect the beam through a small angle (30 minute of an arc) from its original path. If the mirror rotates with a frequency $f\left((5/3)\times {10}^{4}Hz\right)$ and the speed of light is given as $3\times {10}^{8}m/\sec$, the value of D (Where D is distance between rotating mirror and fixed mirror) is $\left(\frac{5}{4}\alpha \right)m$ then the value of $\alpha$ is