Trip times and path differences

What's the difference between trip times and path differences?

The concept of trip time is introduced in the Physics Narrative for this episode and this might be a new idea for you. Furthermore, it is quite likely that you have previously come across the idea of path differences in thinking about and explaining phenomena such as Young's fringes. So, what's the difference between the two?

In relation to explaining Young's fringes there is no real difference in thinking in terms of either trip times or path distances. If light rays pass through the two slits and take the same time to travel to a point on the screen (often by travelling the same distance to a point on the screen), then they will arrive at that point in step and constructive interference, creating a bright fringe on the screen. Because the speed of light is constant, the analyses in terms of time or distance lead to the same outcome.

So things might seem balanced, but we believe that the advantage, even here, rests with the time-based description. If you get back to basics – that is back to do like me, but later – then you should notice that it's all about the time. For two contributions to add (superpose constructively), it's the relationship between their laters that's important.

The value of an approach using trip time becomes even clearer when analysing a situation where the speed of light changes due to the light travelling through different media. Thus in the case of refraction the actual path taken by a ray of light as it passes through, say, a prism, can be identified as the one that takes least time.

The big advantage in thinking about trip times is that this single idea can be used to account for a whole list of phenomena, including reflection, refraction and interference.