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# Dispersion of Light and the Formation of Rainbow

Aug 18, 2023

### Visible Light:

Visible light from the Sun comes to Earth as white light traveling through space in the form of waves. Visible light contains a mixture of wavelengths that the human eye can detect. Visible light has wavelengths between 0.7 and 0.4 millionths of a meter. The different colors you see are electromagnetic waves with different wavelengths. Red light has the longest wavelength. Blue light has the shortest wavelength.

Fig-1: Visible light

#### Explanation:

Transparent mediums like water, different glasses, and transparent plastics bend the light by a different amount known as refraction. Different wavelengths are refracted in different amounts.

A triangular glass prism has two triangular bases and three rectangular lateral surfaces.

The angle between its two lateral surfaces is called the angle of the prism (A).

Fig-2: A prism

When a ray of light falls on one side of a prism, the light ray refracts through the prism and emerges out of it.

Fig-3: Refraction of light through a prism

Sir Isaac Newton observed in the late 1600s that sunlight passing through a prism emerged as bands of different colors. He called these colors a spectrum.

Visible light is made of wavelengths of seven different colors. On passing through a prism, each wavelength is refracted at a different angle and produces a different band of colors known as a spectrum.

Fig-4: Dispersion of light and visual spectrum of light

Long, red wavelengths are bent the least, and short, violet wavelengths are bent the most. When all the wavelengths of visible light combine, they produce white light.

The phenomenon of splitting white light into its constituent colors is called dispersion of light. Here it is due to the refraction of white light by a prism.

White light, on dispersion, splits up into 7 colors, namely violet, indigo, blue, green, yellow, orange, and red. This pattern of colors in the spectrum can be remembered easily by using the acronym VIBGYOR.

### Cause of Dispersion:

Different colors of light bend through different angles w.r.t. the incident ray as they pass through the prism, i.e., the angles of deviation are different for different colors.

Red light bends the least, whereas violet light bends the most.

This is because red light has the longest wavelength and violet light has the shortest wavelength.

Even if the wavelengths of different colored lights are different in the prism, their frequency is the same.

The speed of a wave is given by v = λν.

This means that the speed of red light is the highest and the speed of violet light is the lowest in the prism.

#### Formation of a Rainbow:

When all the wavelengths contained in white light are separated, we see them as different colors. This happens when white light passes through raindrops.

Fig-5: Formation of a rainbow

A rainbow is a natural spectrum that appears in the sky after a rain shower. Dispersion of sunlight by the tiny water droplets present in the atmosphere forms a rainbow. Here, the water droplets act as small prisms and disperse light.

#### Summary

• Visible light from the Sun comes to Earth as white light, traveling through space in the form of waves. Visible light contains a mixture of wavelengths that the human eye can detect.
• Visible light is made of wavelengths of seven different colors. On passing through a prism each wavelength is refracted at a different angle and produces a different band of colors known as a spectrum.
• Red light has the longest wavelength. Blue light has the shortest wavelength.
• The phenomenon of splitting white light into its constituent colors is called dispersion of light.
• This means that the speed of red light is the highest and the speed of violet light is the lowest in the prism.
• Dispersion of sunlight by the tiny water droplets present in the atmosphere forms a rainbow.

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