Question

In the visible spectrum the colour having the shortest wavelength is
A. Green
B. Red
C. Violet
D. Blue

Answer 1

Hint:When white light enters into a refracting surface it gets scattered into seven different colours. The combination of these colours is called a spectrum. According to Rayleigh’s Law of scattering, the extent of scattering of a light is inversely proportional to its wavelength.

Complete answer:
Electromagnetic waves are those in which there is a sinusoidal variation of electric field vector $(\overrightarrow{E})$ and magnetic field vector $(\overrightarrow{B})$ in a direction perpendicular to the direction of propagation of the wave.

The electromagnetic waves exist in an enormous range of frequencies, the systematic distribution of electromagnetic waves in increasing or decreasing order of their frequency or wavelength is called the electromagnetic spectrum. The waves of frequency $4\times {10}^{14}$ to $8\times {10}^{14}$ are called visible rays or simply light. It can be seen by humans and other living beings. Its wavelength lies between $700nm$ and $400nm$.

When the visible light passes through a medium of a high refractive index it gets deflected from its path. The extent of deflection depends on the size of the particles of the medium. This phenomenon is called the scattering of light. Smaller particles scatter light of smaller wavelengths while larger particles scatter light of longer wavelengths.

Now according to Rayleigh law of scattering, the intensity of light of wavelength $\lambda$ present in the scattered light is inversely proportional to the fourth power of $\lambda$ , provided the size of scattering particles is smaller than $\lambda$ , Mathematically
$scattering\propto {\displaystyle \frac{1}{{\lambda }^4}}$

Different colours have different wavelengths. So, a white light on scattering gives a band of seven colours which is called the visible spectrum. Now, we know that the order of visible spectrum is Violet, Indigo, Blue, Green, Yellow and Red (VIBGYOR) that is Violet colour appears at the bottom or we can say that it is the most scattered. So, according to Rayleigh’s Law, we see that violet has the shortest wavelength. (Scattering is inversely proportional to wavelength)

Hence, option C is the correct answer.

Additional information:
The bluishness of sky and reddishness of the sky can be explained by Rayleigh’s Law. Blue colour has the shortest wavelength so it is scattered in all directions by small particles thus the sky appears blue while red colour having the longest wavelength is scattered by larger particles like dust, also during sunrise and sunset, light has to travel larger distance due to which blue, violet and other colours are completely scattered away and only red and yellow colour reaches our eyes that’s why the sky appears reddish during sunrise and sunset.

Note:Rayleigh scattering is the result of the electric polarizability of the particles. Light is an electromagnetic wave so it has an electric and magnetic field oscillating perpendicular to the direction of light, the electric field of the light wave acts on the charges within a particle and makes them move at the same frequency. These particles then become small radiating dipoles whose radiation we see as scattered light.