Question

If the speed of light is $3.0\times {10}^{8}m{s}^{-1}$, calculate the distance covered by light in 2.00ns.

Answer 1

Hint: Recollect the basic concepts. We have been the speed of light in meters per second. We need to calculate the distance covered by light in 2 nanoseconds. Find out the conversion factor between one second and one nanosecond. Then use the formula, $\text{speed=}{\displaystyle \frac{\text{distance}}{\text{time}}}$ and just substitute the values and calculate the distance covered to get the answer.

Complete step by step solution:
- Speed of light is the distance covered by light in unit time.
- Speed is given by the formula,
$$\text{Speed =}{\displaystyle \frac{\text{distance}}{\text{time}}}$$
- We have been given speed of light in meters per second that is, $3.0\times {10}^{8}m{s}^{-1}$. We need to calculate the distance covered by light in 2ns. So, time taken by light to cover a certain distance is 2ns.
- Therefore, $\text{Distance = Speed }\times \text{ Time}$ ……(1)
- Now, speed of light is given in terms of meter per second but time is given in terms of nanoseconds.
- We know that, $1ns={10}^{-9}s$ and therefore, $time=2ns=2\times {10}^{-9}s$
- Substituting the values of speed and time in equation (1) we get,
$$\begin{array}{rl}& \text{Distance = Speed }\times \text{ Time}\\ & \text{=3}\times \text{1}{\text{0}}^{8}m{s}^{-1}\times 2\times {10}^{-9}s\\ & =0.6m\end{array}$$
- Therefore, the distance covered by light in 2ns is 0.6meter.

- Hence, if the speed of light is $3.0\times {10}^{8}m{s}^{-1}$, then the distance covered by light in 2.00ns is 0.6m.

Note: Remember light travels at the speed of 3lakh kilometres per second or $3.0\times {10}^{8}m{s}^{-1}$. Speed of light is defined as the distance covered by light per unit time. It is a directionless quantity. Velocity is analogous to speed which is displacement per unit time but it is a vector quantity and has a particular direction.