Question

Why is the ratio of the velocities of light of wavelengths $4000\mathop A\limits^ \circ {\text{ }}and{\text{ }}8000\mathop A\limits^ \circ$ in vacuum $1:1$?

Answer 1

As we all know, the speed of light in vacuum is $3 \times {10^8}m.{s^{ - 1}}$ . Speed of light in vacuum doesn’t depend on the wavelength or the frequency. The lights contain different wavelengths and also have the same speed in vacuum is $3 \times {10^8}m.{s^{ - 1}}$ .

Complete step by step answer:
Since light is an electromagnetic wave and it is the property of all the electromagnetic waves that they travel with the same speed equal to $3 \times {10^8}m.{s^{ - 1}}$ in vacuum.
Hence, the ratio of the velocities of light of wavelengths $4000\mathop A\limits^ \circ {\text{ }}and{\text{ }}8000\mathop A\limits^ \circ$ in vacuum $1:1$ .
In a vacuum, the speed of light does not rely on frequency (or wavelength). When light travels through a medium other than a vacuum, it travels at a slower rate than when it travels through a vacuum. It's possible that the speed of light varies depending on the wavelength when travelling through a medium.
But they all travel at the same speed in vacuum, which is something they all have in common. Because EM waves of different frequencies propagate at varying speeds through material, the qualification 'in vacuum' is used. The frequency $f$ , the wavelength $\lambda$ , and the speed of light $c$ ,of a wave are all connected according to $c = \lambda f$ .
In general, we say that light travels in waves, and that all electromagnetic radiation travels at the same speed through a vacuum, which is approximately $3 \times {10^8}m.{s^{ - 1}}$ . Nothing can move faster than the speed of light, which is what we call it.

Note:
Electromagnetic waves show electric and magnetic fields. There is no requirement for a medium to display the influence of an electric or magnetic field. EM waves travel in vacuum in the presence of electric and magnetic field vectors that vibrate perpendicular to each other and cause pertervation.