Question

How does the Doppler effect change the appearance of emitted light?

Answer 1

Hint: First of all the appearance of light depends on its wavelength or frequency. In the Doppler effect, the relative motion between the source of light and observer or detector of light will cause variation in its frequency and wavelength. This is the basic idea of changing the appearance of emitted light as a result of the Doppler effect.

Complete answer:
The Doppler effect is the change in frequency of a wave due to the relative motion between source and observer

We have the formula for Doppler effect in non-relativistic case of light as,\[f' = (1 \pm \dfrac{u}{c})f\]
Where $f'$ -observed frequency of light
$f$ -actual frequency of light
$u$ -relative velocity between source and observer
$c$ -velocity of light in free space $ = 3 \times 10^8 m/s$
The positive sign in the expression comes if the distance between the source and observer is decreasing and negative sign comes if the distance between the source and observer is increasing.
Now, let us take an example of moving source away from the source $f' = (1 - \dfrac{u}{c})f$, in this case, the observed frequency decreases or we can say the observed wavelength increases and say that it causes Red shift. If the light source is moving close to the observer, $f' = (1 + \dfrac{u}{c})f$ , in this case, the observed frequency increases and we can say it as a Blue shift. This is how the appearance of emitted light waves changes as a result of the Doppler effect.
One of the basic and important assumptions that we made after considering all these points is “Universe is expanding”. It's based on, Stars emit light, which is why we see them at night. Galaxies are huge collections of stars. Edwin Hubble, an astrophysicist, measured the Doppler shift of a large sample of galaxies. He found that the light from distant galaxies is redshifted. It shows the galaxies are moving away from us, which means our universe is expanding.

Note: If we are considering the Relativistic Doppler effect, i.e, the relative velocity is in the range of velocity of light, then the equation will be modified as $f' = \dfrac{{f\sqrt {1 + \dfrac{{{u^2}}}{{{c^2}}}} }}{{1 - \dfrac{u}{c}\cos \theta }}$
$\theta = 0^\circ$ if the distance between source and observer is decreasing
$\theta = 180^\circ$ if distance between source and observer is increasing