light emitted from a source residing within a weaker gravitational field as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions. Redshift formulae In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of ) is independent of the wavelength. Doppler effect If a source of the light is moving away from an observer, then redshift () occurs; if the source moves towards the observer, then blueshift () occurs. This is true for all electromagnetic waves and is explained by the Doppler effect. Consequently, this type of redshift is called the Doppler redshift. If the source moves away from the observer with velocity , which is much less than the speed of light (), the redshift is given by (since ) where is the speed of light. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency. A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the relativistic Doppler effect. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the time dilation of special relativity which can be corrected for by introducing the Lorentz factor into the classical Doppler formula as follows (for motion solely in the line of sight): This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives–Stilwell experiment. Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the projection of the movement of the source into the line-of-sight which yields different results for different orientations. If is the angle between the direction of relative motion and the direction of emission in the observer's frame (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes: and for motion solely in the line of sight (), this equation reduces