This paper reveals a mysterious law governing the Doppler effect of light. A new exponential term isintroduced: eV/c . Einstein's thought experiment ( chasing a beam of light ) is very compelling and can beconsidered as self-evident. It is an immediate consequence of the non-existence of light carrying medium( ether). The speed of light should be constant c independent not only of source velocity, but also ofobserver velocity. However, Einstein made a serious mistake when he tried to explain this. Hemisinterpreted the constancy of the speed of light as the relativity of space and time. This is anextraordinary, farfetched claim. Therefore, relativistic Doppler effect formula is based on a wrongfoundation. Moreover, all existing theories of light ( special relativity, ether theory, emission theory) failto explain Doppler effect for source- observer relative velocities greater than the speed of light. Althoughspecial relativity imposes that no ( relative ) velocity is greater than the speed of light, it is easy to obtainrelative velocities greater than the speed of light without violating the universal speed limit. This can bedone by an arrangement consisting of light source, observer and a mirror. Suppose that a light source andan observer are at rest relative to each other and located close to each other. Light emitted by the sourcegoes to a distant mirror and is reflected back to the observer, while the mirror is moving towards thesource and observer with velocity close to the speed of light. In this case, the velocity of the mirror imageof the source relative to the observer is equal to 2c, for which the relativistic Doppler effect formula willbe undefined because β = V/c will be greater than 1, resulting in a square root of a negative number.Theoretically, it is possible to get unlimited relative velocity between the mirror image of the source andthe observer by using multiple moving mirrors. Therefore, a new theory of the real law governing theDoppler effect of light is required. Einstein's thought experiment can be understood as the constancy ofphase velocity, not group velocity. The phase velocity of light is always constant c irrespective of sourceand observer motion. The group velocity of light behaves in a more conventional way: it is independent ofsource velocity, but dependent on observer velocity. The constancy of the phase velocity requires,unconventionally, not only change in frequency, but also change in wavelength for a moving observer.Even though this is also counter intuitive, it is not as farfetched as 'length contraction and time dilation'.Therefore, λ . f = λ’. f ’ = c . This theory invokes another problem: then what is the law governing theDoppler effect of light. The new law of Doppler effect of light is proposed as: f ‘ = f . e V/ c , λ’ = λ . e -V/ c, where V is positive for source and observer approaching each other. This theory explains the Ives-Stilwell experiment.