Which of the following statements correctly describes the relationship between wavelength and frequency for visible light in the range of 400 to 700 nm?

• A. Wavelength and frequency are independent of each other in visible light.
• B. Both wavelength and frequency increase together in visible light.
• C. As the wavelength increases from 400 nm to 700 nm, the frequency increases.
• D. As the wavelength increases from 400 nm to 700 nm, the frequency decreases.

Answer: (D)

Verified step by step guidance

1. Recall the fundamental relationship between the speed of light (\(c\)), wavelength (\(\lambda\)), and frequency (\(\nu\)), which is given by the equation: \(c = \lambda \times \nu\).
2. Understand that the speed of light in a vacuum is a constant, approximately \$3.00 \times 10^{8}$ meters per second, so any change in wavelength must result in an inverse change in frequency to keep the product constant.
3. Recognize that visible light wavelengths range from about 400 nm (violet) to 700 nm (red), and as the wavelength increases within this range, the frequency must decrease to maintain the constant speed of light.
4. Analyze the options given: since wavelength and frequency are inversely related, they cannot both increase together, nor are they independent; therefore, the correct description is that frequency decreases as wavelength increases.
5. Summarize that the correct relationship for visible light between 400 nm and 700 nm is: as wavelength increases, frequency decreases, consistent with the equation \(\nu = \frac{c}{\lambda}\).