If distance between the wheel and mirror is ' d ' then the...

If distance between the wheel and mirror is ' $d$ ' then the velocity of light is : (Given that $m$ be the number of teeth and ' $n$ ' the number of revolutions made in one second).
(a) $\mathrm{mnd}$
(b) $2 \mathrm{mnd}$
(c) $3 \mathrm{mnd}$
(d) $4 \mathrm{mnd}$

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Key Concepts

Rotating Cog Wheel Experiment

This method uses a rotating wheel with evenly spaced teeth to intermittently block and pass a beam of light. As the wheel rotates, the timing of the light passage is related to the gaps between the teeth. By synchronizing the rotation speed with the light’s round?trip travel time to a distant mirror, one can deduce the speed of light from the observed conditions under which light is blocked or transmitted.

Relation Between Rotation and Time Delay

In this technique, the rotational speed of the wheel (expressed by the number of revolutions per second and the number of teeth) directly provides a measure of the time interval between successive gaps or obstructions. This time interval, when equated to the time taken for light to travel a known distance to a mirror and back, allows the calculation of the speed of light using the relationship between distance, time, and rotational frequency.

Speed of Light

This is a fundamental constant that represents the fastest speed at which energy, matter, or information can travel in the universe. It has been historically measured using various experimental techniques, each designed around timing the extremely short intervals required for light to traverse a known distance.

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