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Chapter 6: Problem 5

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

Expert verified
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

01

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.
02

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).
03

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.
04

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.

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