Use the relativistic Doppler formula for light emitted

In summary, the relativistic Doppler formula is a mathematical equation that calculates the change in frequency of light emitted by a source moving at a high velocity relative to an observer. It differs from the classical Doppler formula by taking into account the effects of special relativity. The Lorentz factor is a key component of the formula and is used to adjust the observed frequency based on the relative velocity between the source and observer. The formula can be used for any type of electromagnetic radiation and has many real-world applications in fields such as GPS technology, astronomy, and medical imaging. It also plays a significant role in confirming the principles of special relativity and expanding our understanding of the universe.
  • #1
eit32
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6) Using Hubble’s law, estimate the wavelength of the 590 nm sodium line emitted from galaxies (a) 2*10^6 lightyears away from Earth, (b) 2*10^8 lightyears away, and (c) 2*10^9 lightyears away.
** Use the relativistic Doppler formula for light emitted from a receding source)
 
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  • #2
You should probably post an attempt at solving..

Start by using Hubble's law to find the recession velocity at each distance then use the relativistic doppler formula to find the wavelength shift for each.
 

1. What is the relativistic Doppler formula for light emitted?

The relativistic Doppler formula is a mathematical equation used to calculate the change in frequency of light emitted by a source moving at a high velocity relative to an observer. It takes into account the effects of special relativity, such as time dilation and length contraction, on the observed frequency of light.

2. How does the relativistic Doppler formula differ from the classical Doppler formula?

The classical Doppler formula, also known as the non-relativistic Doppler formula, is based on the assumption that the source and observer are both stationary. The relativistic Doppler formula, on the other hand, takes into account the relative motion between the source and observer, as well as the effects of special relativity on the observed frequency of light.

3. What is the significance of the Lorentz factor in the relativistic Doppler formula?

The Lorentz factor, denoted as γ (gamma), is a key component of the relativistic Doppler formula. It represents the factor by which time and length are affected by an object's velocity and is a fundamental concept in special relativity. In the relativistic Doppler formula, the Lorentz factor is used to adjust the observed frequency of light based on the relative velocity between the source and observer.

4. Can the relativistic Doppler formula be used for any type of light, such as radio waves or visible light?

Yes, the relativistic Doppler formula can be used for any type of electromagnetic radiation, including radio waves, visible light, and even gamma rays. This is because all forms of electromagnetic radiation travel at the same speed in a vacuum, the speed of light (c), and are subject to the same effects of special relativity.

5. How is the relativistic Doppler formula used in real-world applications?

The relativistic Doppler formula has many practical applications, such as in GPS technology, where it is used to account for the effects of relativity on satellite signals. It is also used in astronomy to calculate the redshift of distant galaxies and in medical imaging to adjust for the Doppler effect in ultrasound imaging. Additionally, it has been used in experiments to confirm the principles of special relativity and has important implications for our understanding of the universe.

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