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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 outward from the innermost band of the rainbow? (b) Does the frequency of light increase or decrease as we proceed outward? [Section 6.3]

Short Answer

Expert verified
(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 by step solution

01

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.
02

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.
03

(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.
04

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.
05

(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.

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