Question

How many nanoseconds does it take light to travel 1.00 ft in vacuum?

Short answer

Light takes1.016 nanoseconds to travel 1 ft distance in vacuum

Step-by-step solution

Speed of light in vacuum

Here,

Light when travels through the vacuum it has maximum speed. The speed of light in vacuum is $3\times {10}^8$m/s. No object in the universe can travel more than this speed.

V= Velocity of light in vaccum (m/s)

D = Distance travelled by light (m)

T = Time taken (s)

Given data

Distance in ft = 1 ft

D = 0.3048 meter

V= $\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\raisebox{1ex}{$\mathbf{m}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{s}$}\right.$( speed of light in vaccum)

Calculation of time in nanoseconds

Since, Formula of speed of light is the ratio of distance travelled by the light to the time taken to travelle that distance.

$$\begin{gathered} \mathrm{velocity}\left(\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.\right)=\frac{\mathrm{distance}\left(\mathrm{m}\right)}{\mathrm{time}\left(\mathrm{s}\right)} \\ 3\times {10}^8=\frac{0.3048m}{T} \\ T=\frac{0.3048m}{3\times {10}^8} \\ T=0.1016\times {10}^{-8}S \\ T=1.016\times {10}^{-9}S \\ T=1.016nS \\ 1nS={10}^{-9}S \end{gathered}$$

Hence from the above calculation it seems Light takes1.016 nanosecondsto travel 1 ft distance in vacuum