# Video: Understanding Light-Years

A laser beam was fired off into space from an observatory on Earth’s surface. The beam was fired into an empty region of space, so it would not interact with anything. How far, in light-years, has the beam travelled 3 years later?

02:08

### Video Transcript

A laser beam was fired off into space from an observatory on Earth’s surface. The beam was fired into an empty region of space, so it would not interact with anything. How far, in light-years, has the beam travelled three years later?

Okay, so in this question, we’ve got an observatory on the surface of the Earth which fires a laser beam off into space. Now we’ve been told that this beam of light is fired into an empty region of space so it doesn’t interact with anything. In other words, the beam just keeps going at the same speed for a very long time. And we’ve been asked to find the distance, in light-years, travelled by the beam in a period of three years.

So let’s say, first of all, that this is the distance that we’re trying to find. In other words, a beam fired from here, three years later is this far from the Earth. Now, naturally, this diagram is absolutely not to scale. But that doesn’t really matter. It shouldn’t hinder us from calculating the correct value. So let’s call the distance that we’re trying to calculate 𝑑. And let’s also recall the definition of a light-year. We can recall that one light-year is the distance travelled by light in a vacuum in one year. Now, in this scenario, we’ve basically got the light travelling in a vacuum for almost its entire journey.

We say almost because, of course, when the laser was fired from the surface of the Earth, for a very short period of time, it was travelling through the atmosphere of the Earth. However, the atmosphere does not massively slow down any light travelling through it. And even if it did, this distance is so small that compared to the total distance travelled in a vacuum, we can ignore it completely. We don’t need to worry about it. In other words, we can safely say that the distance that we’re trying to calculate, 𝑑, is basically equivalent to if the light had travelled through a vacuum for its entire journey. We can ignore any atmospheric effects.

So with that in mind, we know that one light-year is the distance travelled by light in a vacuum in one year. And so, three years after the laser was fired, because the light is travelling in a vacuum, the light will have travelled a distance of three light-years. In other words, in the first year of the light’s journey, the light will have travelled a distance of one light-year. In the second year of the light’s journey, by definition, the light would have travelled another light-year. And then, finally, in its third year of travel, it would have travelled a third light-year. And so, essentially, this question is asking us how many light-years does a light travel in three years. And the answer to that is three light-years.