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Question: If the speed of light is \(3.0\times {{10}^{8}}m{{s}^{-1}}\), calculate the distance covered by ligh...

If the speed of light is 3.0×108ms13.0\times {{10}^{8}}m{{s}^{-1}}, calculate the distance covered by light in 2.00ns.

Explanation

Solution

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, speed=distancetime\text{speed=}\dfrac{\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,
Speed =distancetime\text{Speed =}\dfrac{\text{distance}}{\text{time}}
- We have been given speed of light in meters per second that is, 3.0×108ms13.0\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, Distance = Speed !!×!! Time\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=109s1ns={{10}^{-9}}s and therefore, time=2ns=2×109stime=2ns=2\times {{10}^{-9}}s
- Substituting the values of speed and time in equation (1) we get,

& \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{aligned}$$ \- 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.