 Let's start with Alice. So in her frame, the light clock is stationary. So when the photon is moving towards the right, it's traveling at speed C, the clock has meant LA, so it'll take LA over C. And the same for the trip to the left. Therefore, TA is given by 2 LA on C. Okay, now let's look at things from Bob's reference frame. The two mirrors are initially separated by a distance LB. Now the photon is moving to the right at speed C, but the rightmost mirror is moving away from the photon at speed V. Therefore, the time it'll take the photon to reach the right mirror is LB divided by C minus B. On the way back, again, they're initially separated by LB, but the photon is moving to the left at speed C and the mirror is moving towards at speed V. And so the time taken is LB on C plus V. Now we can simplify this like this. So it's always good to get into a habit of checking your work. So I've got this expression here. Is there anything we can quickly do to see if it's obviously wrong? Well, in our everyday life, we don't notice special relativity effects. Everything works according to Newton's equations, when the velocity is much smaller than C. So let's see what would happen if V was much, much smaller than C. Then the denominator C squared minus V squared would be pretty much just equal to C squared. And in this case, we get a result that looks similar to the result TA. This is a good sign because in Newtonian mechanics, you know, before we've heard any of this strange special relativity, we'd expect Alice and Bob to measure the same times for the ticking of the light clocks. Okay, I am going to take the answer we got and I'm going to write it in a very suggestive manner like this. So because of time dilation, as we derived in the previous section, Alice's clock will be ticking more slowly than Bob's. So we've got an equation that looks like this and there's a gamma involved. So think about it, if Alice's clock is ticking more slowly and gamma is greater than one, which side of the equation should gamma be on? Pause the video and see if you can guess. Okay, so if Alice's clock is ticking more slowly, when Alice says one second elapsed, Bob will say no, more than one second elapsed. So gamma should be on the left hand side. This is the expression. It's always a good idea if you can to try and get some intuition for these equations, that way you're not stuck having to look through a formula sheet every time you come across any problem and gamma is of course given by this. So here's a question. How do LA and LD relate to each other? Give it a try and if you get stuck, there's a hint in the next video.