Turning Points question on Fizeau’s experiment

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julsusxx
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* d = distance from M (mirror) to W (rotating toothed wheel) = 8.6km
* f = number of wheel revolutions per second = 12
* n = number of teeth in wheel = 720
* c = speed of light = 4dnf

Question : The speed of the wheel is further increased. Deduce the value of f when the observer would next be unable to see the light returning from the mirror.

The answer is 36. Why?
P.S. When my teacher explained the answer to me I understood it, but now my friends have counteracted his answer with a reasonable explanation and I’m confused again
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Joinedup
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Presumably at 12 rpm the reflected light is hitting the first tooth after the gap it shone out through. If you doubled the speed to 24 it'd come back through the gap following that tooth and the next speed it would be blocked would be 36 when it was hitting the second tooth after the gap it shone out through.

Don't think I can really help properly without knowing about the incorrect reasoning that you think is more convincing
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julsusxx
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Their argument was basically because they took 12 as being the frequency, and because 36 is a multiple, the wheel is still doing a complete turn so would end in the same place it started. They initially thought the answer would be 24 if that was the case, do you think you could clear up our confusion?
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(Original post by julsusxx)
Their argument was basically because they took 12 as being the frequency, and because 36 is a multiple, the wheel is still doing a complete turn so would end in the same place it started. They initially thought the answer would be 24 if that was the case, do you think you could clear up our confusion?
Well Fizeau did a lot of different experiments afaik but it seems like you're being asked about this set up

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The wheel has a number of identical teeth and slots around its circumfrence.
as the wheel rotates slowly the following things are happening
1. the light from the source is alternately being blocked by the teeth and allowed to pass through the slots - a series of light pulses is being sent out towards the mirror.
2. your view of the mirror is alternately being blocked by the teeth and revealed by the slots.

with the wheel rotating slowly you can see the light source reflected in the distant mirror. what is happening is that the light is completing the round trip before the next tooth has moved far enough to block your view of the mirror.
The light pulses have a short time of flight for the two way trip to the distant mirror - but it's not instant.
if the speed of the wheel is increased further the wheel will at some speed rotate far enough during the flight of each pulse that the last pulse arrives back when the slot has rotated away and the next tooth is blocking your view of the distant mirror - you won't be able to see the light being reflected in the distant mirror.

if the speed is increased further you'll see the returning light pulses through the slot after the one the outgoing pulse went through

and if you increase it further still, the return pulses will be blocked by the tooth after that slot

and so on.

This doesn't involve the wheel making complete revolutions in the time it takes for the light to make the return trip - for the first speed at which you can't see the returning light it's the time to rotate between one of the slots and the tooth after it.
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