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**34.1. LIGHT INTENSITY, DISTANCE AND (C+V) (C-V) MATHEMATICS**

It is a well-known topic that light intensity changes depending on distance. As you move a circle from the light source, amount of light that passes through it in a unit of time decreases. The figure below shows this.

The general rule is as follows: Intensity of a light that a point source emits around it decreases inversely proportional to the square of the distance. We can think that in practice when we double the distance, the light intensity will decrease fourfold. There is the following equation in line with this rule.

Since Light Intensity is a result primarily based on the number of photons that make up the light, we can write the equation above by presenting the real reason as below:

However, both equations above are valid for targets that are not in motion relative to light source. When there is movement, (c+v) (c-v) mathematics steps in the situation.

We can see how (c+v) (c-v) mathematics interferes in the figure below. Think of an object that stands still at
d_{0} distance to the light source. The fact that the object is drawn as a round shape is not important. Assume that n of the photons that are emitted at a time such as
t_{0} choose this object as their arrival targets. As a result, n number of photons cover
d_{0} distance in t_{Δ} =d_{0}/c time and reach their target objects. Now, let’s think of the situation the object moves away. When the object is at
d_{0} distance, n number of photons again choose the object as their arrival target and set out towards it. However, this time, the speed of the photons is (c+v) and these photons will arrive at the object at
d_{1} distance instead of d_{0} distance and the number of photons will not change. In case the object comes to the light source, photons will reach the target, which travels at (c-v) speed, at
d_{2} distance and the number of photons will, again, not change.

The fact that the number of photons does not change doesn’t mean that the object will get the same light intensity in all these cases because energies of the photons will change although their numbers stay the same.

The change in the energy will be directly proportional to wavelength change.

Therefore, we can define the equation: E_{X} . λ_{X} = E_{0} . λ_{0}. Then, an object that receives
E_{0} amount of energy will receive E_{2}= E_{0}.c/(c+v) energy if it is in motion and if it is moving away, and it will receive
E_{1}= E_{0}.c/(c-v) if it is approaching. In the figure, pay attention to the fact that
d_{1} and d_{2} distances are determined by t_{Δ} time. The number of photons not changing is directly related to t_{Δ} time. The number of photons will change when the t_{Δ} time is exceeded.

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