A planar structure of length L and width W is made of two different optical media of refractive indices $\mathrm{n}_1=1.5$ and $\mathrm{n}_2=1.44$ as shown in figure. If $\mathrm{L} \gg \mathrm{W}$, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For $\mathrm{L}=9.6 \mathrm{~m}$, if the incident angle $\theta$ is varied, the maximum time taken by a ray to exit the plane CD is $\mathrm{t} \times 10^{-9} \mathrm{~s}$, where t is $\_\_\_\_$ .
[Speed of light $\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ]