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The Doppler effect is a crucial physical phenomenon that describes how the frequency of a wave changes when the observer and the source are in motion relative to each other. This effect is observed in all types of waves, including sound and light waves. When the source moves closer to the observer, the waves compress, leading to an increase in frequency, which we perceive as a shorter wavelength (blueshift). Conversely, when the source moves away, the waves stretch, resulting in a decrease in frequency and a longer wavelength (redshift). This principle is fundamental in astrophysics for determining the motion and velocity of astronomical objects by analyzing the shifts in wavelengths of known spectral lines.

Redshift occurs when the light from an object is shifted towards longer wavelengths. In the context of stars and galaxies, redshift indicates that the object is moving away from the observer. This shift to longer wavelengths happens as a result of the Doppler effect, which stretches the light wave as the object recedes. The higher the redshift, the faster the object is moving away. We calculate redshift using the formula: \( \frac{Δλ}{λ} = \frac{v_{rad}}{c} \) where \(Δλ\) is the change in wavelength, \(λ\) is the original wavelength, \( v_{rad} \) is the radial velocity, and \( c \) is the speed of light. Applying this formula helps infer the velocity of stars and galaxies from their observed spectral lines, providing valuable information about the universe's expanding nature.

The Balmer series refers to a sequence of spectral lines emitted by hydrogen atoms when electrons transition from higher energy levels to the second energy level. Named after Johann Balmer, this series is visible in the optical part of the spectrum, typically manifesting as prominent lines that can be observed with telescopes. Among these lines, the Balmer beta line is one pivotal feature, occurring at a wavelength of 486.1 nm in a laboratory setting. By comparing this laboratory wavelength to the wavelengths observed in a star's spectrum, astronomers can determine if the star is moving towards or away from us (via blueshift or redshift) and calculate its radial velocity. For example, observing the Balmer beta line at 486.3 nm in a star's spectrum implies a redshift and indicates the star is receding.