Question

In vacuum what will be common among X-rays, visible light, radio waves, and infra-red rays?
A. Speed
B. Frequency
C. Wavelength
D. Amplitude

Answer 1

Hint: The refractive index of the given medium is the ratio of speed of electromagnetic wave in vacuum to the speed of electromagnetic wave in the given medium. The refractive index of the vacuum is 1. Recall the relation between speed, wavelength and frequency of the electromagnetic wave to answer this question.

Complete answer:
To answer this question, let’s check every option one by one as follows, we know that the refractive index of the given medium is the ratio of speed of electromagnetic wave in vacuum to the speed of electromagnetic wave in the given medium. Therefore,
\[\mu = \dfrac{c}{v}\],
Where, v is the speed of electromagnetic waves in the given medium.

We know that the refractive index of the vacuum is 1. Therefore,
\[1 = \dfrac{c}{v}\]
\[ \Rightarrow v = c\]

Therefore, for any type of electromagnetic radiation such as X-rays, visible light, radio waves, and infra-red rays, the speed will remain the same that is the speed of light. Therefore, the option (A) is correct.

We know that the frequency of the radiation depends on which material is producing the given electromagnetic wave. X-rays, visible light, radio waves, and infra-red rays are produced by vibrations of different particles. Therefore, the frequency cannot be the same.
Thus, the option (B) is incorrect.

We know the relation between speed of light, wavelength and frequency.
\[c = f\lambda \], where, f is the frequency and \[\lambda \] is the wavelength.

From the above expression, the wavelength of the EM wave depends on the frequency. Since the frequency of X-rays, visible light, radio waves, and infra-red rays is different, the wavelength of these EM waves must be different. Therefore, the option (C) is incorrect.

We know that X-rays, visible light, radio waves, and infra-red rays carry different energies. The energy of electromagnetic waves is directly related to amplitude. Therefore, the amplitude of these waves cannot be the same.

Thus, the option D is incorrect.

Note: Note that the frequency of the EM wave does not change when the light travels from one medium to another medium. Also, the velocity of the EM wave changes when it travels through a medium of different refractive index. To answer this question, students must refer to the electromagnetic spectrum of light.