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 out-wavelength of light increase or decrease as we proceed out- frequency of light increase or decrease as we proceed out-ward? [Section 6.3]

Short answer

As we proceed outwards in a rainbow, from violet to red, the wavelength of light increases (from shorter to longer wavelengths), and the frequency of light decreases (from higher to lower frequencies).

Step-by-step solution

Recall the relationship between wavelength, frequency, and speed of light

The relationship between the wavelength (λ) and frequency (v) can be described by the equation \(c = λv\), where \(c\) is the speed of light. Thus, if we know how the wavelength or the frequency changes as we move outwards from the center of a rainbow, we can determine how the other quantity changes base on this relationship.

Observe the color sequence of a rainbow

The colors in a rainbow follow the pattern of red on the outer part and violet on the inner part. The colors appear in the following sequence: Red, Orange, Yellow, Green, Blue, Indigo, and Violet (ROYGBIV).

Recall how the wavelength and frequency of light are related to the color

The color of light depends on its wavelength (or frequency). Red light has the longest wavelength and the lowest frequency, whereas violet has the shortest wavelength and the highest frequency. As we progress from red to violet, the wavelength decreases, and the frequency increases.

Determine the change of wavelength and frequency as we proceed outwards in a rainbow

Based on the color sequence (ROYGBIV) and the relationship between color, wavelength, and frequency, we can conclude the following: As we proceed outwards in a rainbow, from violet to red: 1. The wavelength of light increases (from shorter to longer wavelengths) 2. The frequency of light decreases (from higher to lower frequencies) In summary, the wavelength of light increases, and the frequency of light decreases as we proceed outwards in a rainbow.

Key concepts

Rainbow Diffraction

A rainbow is a beautiful natural spectacle that occurs when sunlight passes through tiny droplets of water in the atmosphere. This phenomenon, known as diffraction, splits the light into its component colors, creating a spectrum of colors in the sky.

The diffraction of light in a rainbow is a combination of two processes:

• Refraction: When light enters and exits the water droplet, it bends due to the change in the medium.
• Reflection: Some of the light reflects off the inside surface of the droplet.
• Dispersion: Different colors in the light spectrum spread out due to wavelength variance.

These processes together cause sunlight to separate into a circle of colors — a rainbow. The size and intensity of the rainbow depend on the size of the droplets and the number of reflections inside them.

Light Wavelength

The wavelength of light is a crucial aspect when discussing rainbows and is key to understanding their color formation. Wavelength refers to the distance between two consecutive peaks or troughs of a light wave. It is typically measured in nanometers (nm).

Different colors have different wavelengths:

• Red light has longer wavelengths, around 620-750 nm, making it appear on the outer edge of a rainbow.
• Violet light has shorter wavelengths, approximately 380-450 nm, placing it on the inner edge.

The wavelength of light affects its ability to diffract; shorter wavelengths bend more than longer ones, which is why the colors in a rainbow appear in a specific order.

Light Frequency

Light frequency is another fundamental concept in understanding how rainbows form. It refers to the number of wave cycles that pass a given point per second and is measured in Hertz (Hz). Light frequency is inversely related to wavelength, through the equation: \[c = λv\]where \( c \) is the speed of light. As a light's wavelength decreases, its frequency rises, and vice versa.

In the visible spectrum:

• Violet light has a high frequency because of its short wavelength.
• Red light has a lower frequency due to its longer wavelength.

Understanding frequency helps explain why the colors of the rainbow appear as they do, with violet on the inside where wavelengths are shortest, and red on the outside where wavelengths are longest.

Color Sequence in Rainbows

The color sequence in rainbows is a classic visual and mnemonic tool, often remembered by the acronym ROYGBIV - Red, Orange, Yellow, Green, Blue, Indigo, Violet. This sequence represents the order of colors from the outermost to innermost arc of a rainbow.

Important points about the color sequence:

• Red, the longest wavelength, appears on the outer edge.
• Violet, the shortest wavelength, appears on the inner edge.
• Intermediate colors (Orange, Yellow, Green, Blue, and Indigo) fill in the spectrum, each slightly blending into the next.

The arrangement of colors is a direct result of how differently colored light waves refract and disperse through water droplets. Each hue exhibits a unique wavelength and frequency, contributing to the distinctive and compelling order of a rainbow's colors.