Measuring the Speed of Light by Fizeau method

Light is really really fast, and a light beam travels at a velocity of 299792. 458 km/second. We can say it’s close to 300,000 km/second. The light from the sun reaches us after8 minutes and 20 seconds. This velocity is the same for every colour of light, violet to red, and hence is independent of wavelength or frequency. Measuring this kind of speed was a great challenge for scientists, at that time, using available technology of clocks to measure a time interval. Fizeau showed a brilliant method. He used an experimental setup which from one end to the other end needed 8.6 miles (13.84 km). That’s not much at all, considering that even if we want to measure 1 second time interval in the normal way, we would have to get light to travel 300,000 km.

The video shows that he used a high-speed rotating gear, and the teeth of the gear was placed always in front of a light beam. Imagine you hold a torch in front of a rotating gear teeth. You will see a blinking light at any given rotational speed of gear, and a continuous non-blinking light when the speed of rotation is increased so fast that you can’t differentiate between the breaks. In Fizeau’s method, he made the light travel a long distance, of 8.6 miles x 2 = 17.2 miles. That is always the key to measuring the velocity of light. It gives some breathing time to make some kind of time interval measurement between two points….. not by a direct stop-watch but indirectly.

Coming back to the video, a source of light is shooting a beam. This beam is concentrated into parallel rays by a convex lens as usual. Then this parallel beam strikes an inclined Glass Plate which is transparent.

A question at this point which many may ask - Why Glass? Why not a Mirror?

The reason is that Fizeau wanted the same Glass plate to reflect most of the light beam as well as allow the returning light beam to pass through the glass plate (on the return journey). If we put a mirror there, it won’t allow the light beam to pass through it. Only a glass plate will work. The reflection from a transparent glass plate is possible, as long as it is inclined correctly and of the right material.

Now, the light beam gets reflected due to the incline of the Glass Plate. This reflected light beam is carefully adjusted so that it strikes at the location where there are moving teeth of a rotating gear. See video animation. The light beam will pass through if it arrives at the precise time when the teeth has rotated a bit and there is a gap. If the light beam strikes a tooth at this instant, the light will get blocked, of course.

Let’s say the timing is right, due to a correct rotational speed of gear, and light passes through.

There could be some part of the beam which are off-track, and so once again there is a need to put some convex lens on the way, see video, lens No.2 . This is useful just to get it into a proper shape, and we get a parallel beam coming out. Now, put a convex lens No.3 whose job is to focus this parallel beam on a Mirror. Which means the Mirror central point must be ideally at the focal length of the convex lens No.3.

The light beam has truck the centre of Mirror, and has nowhere else to go, but to get back on the same way it came. So, it will retrace its path backwards, hit the convex lens No.3, then it will hit the convex lens No.2, and hit the gear.

So far, so good. Once again if it hits a solid tooth, the beam gets blocked right there. If it hits a gap between the gear teeth, if finds a way out, and travels straight to hit the Glass Plate.

Now, our famous Glass Plate lets the light beam pass through, since angle of inclination is not a reflecting angle, and the beam has successfully crossed the glass plate. Actually, the light beam at this point , in Fizeau’s experiment had gone 8.6 miles and come back 8.6 miles, a total of 17.2 miles. Oncae again, we need to make the light beam straightened out, so you see another Convex Lens No.4 to make it parallel.

Behind this convex lens No.4 is a telescope , this is just to be able to see the light beam clearly over the huge distance. And we are supposed to be looking through this telescope.

The interruption of light beam by the gear teeth was a brilliant idea of Fizeau. The angular displacement of a single gear teeth is the angular spread it occupies for a time interval. If angular displacement = θfor one teeth , then the angular displacement for a spread of 1 teeth + 1 gap =2θ . If this can be understood, the main concept has been understood. To arrive further at how to get the speed of light , see the derivation of equations explained clearly in the video.

To understand the working, observe the animation and video at various positions the light beam journey.

Trust this was useful to you.