each other. light and hence () Expl...

each other. light and hence () Explain the Doppler effect in light explain the red and blue shift.

JEE/Engineering Exams
4.0 (1 ratings)
Relativistic Doppler Effect for Light Consider two objects: the light source and the "listener" (or observer). since light waves traveling in empty space have no medium, we analyze the Doppler effect for light in terms of the motion of the source relative to the listener. We set up our coordinate system so that the positive direction is from the listener toward the source. So if the source is moving away from the listener, its velocity ( v ) is positive, but if it is moving toward the listener, then the ( v ) is negative. The listener, in this case, is always considered to be at rest (so ( v ) is really the total relative velocity between them). The speed of light ( c ) is always considered positive. The listener receives a frequency ( f_{mathrm{L}} ) which would be different from the frequency transmitted by the source ( f_{mathrm{S}} ). This is calculated with relativistic mechanics, by applying necessary the length contraction, and obtains the relationship: ( f_{mathrm{L}}=operatorname{sqrt}[(c-v) /(c+v)]^{*} f_{mathrm{S}} ) Red Shift & Blue Shift A light source moving away from the listener ( ( v ) is positive) would provide an ( f_{mathrm{L}} ) that is less than ( f_{mathrm{S}} ). In the visible light spectrum, this causes a shift toward the red end of the light spectrum, so it is called a redshift. When the light source is moving toward the listener ( ( v ) is negative), then ( f_{mathrm{L}} ) is greater than ( f_{mathrm{S}} ). In the visible light spectrum, this causes a shift toward the high-frequency end of the light spectrum. For some reason, violet got the short end of the stick and such frequency shift is actually called a blue shift. Obviously, in the area of the electromagnetic spectrum outside of the visible light spectrum, these shifts might not actually be toward red and blue. If you're in the infrared, for example, you're ironically shifting away from red when you experience a "redshift."
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free