Problem 5 - Chemistry: The Central Science in SI Units, Global Edition

Question

The familiar phenomenon of a rainbow results from the diffraction of sunlight through raindrops. (a) Does the wavelength of light increase or decrease as we proceed outward from the innermost band of the rainbow? (b) Does the frequency of light increase or decrease as we proceed outward? [Section 6.3]

Step-by-Step Solution

Answer

(a) As we move from the innermost band (Violet) towards the outer bands (Red) in a rainbow, the wavelength of light increases. (b) As we proceed outward from the innermost band of the rainbow, the frequency of light decreases since the frequency of light is inversely proportional to its wavelength.

Step 1: Color order in a rainbow

A rainbow consists of a series of concentric circular bands of colors. Moving from the innermost band to the outer bands, the colors appear in the following order: Violet, Indigo, Blue, Green, Yellow, Orange, and Red (or VIBGYOR). It's crucial to remember the order in which these colors appear in a rainbow to answer the next steps.

Step 2: Relationship between wavelength and color

Each color in the rainbow corresponds to a specific range of wavelengths in the visible light spectrum. The wavelength increases from violet to red. By understanding this relationship, we can now answer part (a) of the exercise.

Step 3: (a) Wavelength as we proceed outward

As we move from the innermost band (Violet) towards the outer bands (Red), the wavelength of light increases. This is because red light has a longer wavelength than violet light.

Step 4: Relationship between frequency and color

We also need to consider the relationship between frequency and color in the visible light spectrum. The frequency of light is inversely proportional to its wavelength. Thus, as the wavelength increases, the frequency decreases.

Step 5: (b) Frequency as we proceed outward

As the wavelength of light increases from the innermost band (Violet) to the outer bands (Red) of the rainbow, the frequency of light decreases. This is because, as we mentioned earlier, the frequency of light is inversely proportional to its wavelength. In conclusion: (a) As we proceed outward from the innermost band of the rainbow, the wavelength of light increases. (b) As we proceed outward from the innermost band of the rainbow, the frequency of light decreases.

Key Concepts

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. It consists of a range of wavelengths from approximately 400 nm to 700 nm. Each wavelength corresponds to a different color that we can perceive.

Within this spectrum, shorter wavelengths appear at the blue-violet end, while longer wavelengths are seen at the red end. This range includes all the colors visible in a rainbow. For practical purposes, the most important parts of the spectrum are:

• Violet (around 400 nm)
• Indigo
• Blue
• Green
• Yellow
• Orange
• Red (around 700 nm)

Understanding the visible light spectrum is key to grasping how light interacts with different objects, including water droplets in a rainbow. This interaction, known as diffraction, splits the light into these visible colors. When sunlight passes through rain droplets, the light is dissected into its component colors, forming the beautiful phenomenon we call a rainbow.

Wavelength and Frequency

Wavelength and frequency are fundamental concepts in understanding electromagnetic waves, including light. A wavelength is the distance between two consecutive peaks of a wave, measured in nanometers (nm) for visible light.

Frequency, on the other hand, refers to the number of wave cycles that pass a point in one second. It is measured in hertz (Hz).

Wavelength (\( \lambda \)) and frequency (\( f \)) are inversely related, given by the equation:\[ c = \lambda \times f \]
where \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) meters per second.

In the context of a rainbow, as we move from the inner violet band to the outer red band, the wavelength of light increases. Consequently, the frequency decreases because frequency and wavelength are inversely related. Hence, violet light has a short wavelength and high frequency, while red light has a long wavelength and low frequency.

Color Order in Rainbow

The color order in a rainbow is consistent due to the properties of light dispersion through water droplets. This dispersive process splits sunlight into its component colors, each refracted at slightly different angles due to their varying wavelengths.

The classic sequence of colors in a rainbow can be remembered by the acronym VIBGYOR, which stands for:

• Violet
• Indigo
• Blue
• Green
• Yellow
• Orange
• Red

This order is not arbitrary; it results from the way light is bent by the raindrops. Violet bends the most, appearing on the inside of the arc. Red bends the least, forming the outermost part.

Understanding the color order in rainbows helps us appreciate how light behaves when it interacts with different mediums. This natural occurrence beautifully illustrates significant scientific principles about light behavior, wavelength, and frequency, making rainbows an excellent visual aid in understanding optics.