### 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.