8.4   DOPPLER AND TRANSVERSAL DOPPLER EFFECTS

DOPPLER EFFECT:

By definition the Doppler Effect is the variation in the light length when the source or the observer moves for a beam emitted parallel to the movement.

We have already calculated in the previous section the light length when the source moves with velocity u:

λ = λ₀/(1 + u/c)   

The beam can have the same or the opposite direction of the velocity u of the source then u will be positive or negative respectively.

We observe now that λ doesn’t change when the observer moves then:

Note that the color of light could actually be directly related to its energy and not to λ.

TRANSVERSAL DOPPLER EFFECT:

The Transversal Doppler Effect is by definition the variation in the light length when the source moves for a beam detected in a perpendicular direction of the movement.

We must carefully observe that to get a beam that travels in a direction perpendicular to the trajectory of the source it must be emitted a beam backwards such that the resultant velocity is:

ç = c - u

The absolute value of the velocity is then:

ç = (c² – u²)^1/2 = c(1 - u²/ c²) ^1/2

Then the light length is:

λ = h/mç

λ = h/(mc(1 - u²/ c²) ^1/2)

λ = λ₀/(1 - u²/ c²) ^1/2

Then λ is dilated and we have the same transversal Doppler Effect as that proposed by the Relativity Theory.