Which of the following best describes the relationship between the frequency (ν) and wavelength (λ) of light?

• A. They are directly proportional; as wavelength increases, frequency increases.
• B. They are unrelated; changing wavelength does not affect frequency.
• C. They are inversely proportional; as wavelength increases, frequency decreases.
• D. They are both constant for all types of light.

Answer: (C)

Verified step by step guidance

1. Recall the fundamental relationship between the speed of light (c), frequency (\( \nu \)), and wavelength (\( \lambda \)) given by the equation: \[ c = \nu \times \lambda \] where \( c \) is the speed of light, approximately \( 3.00 \times 10^{8} \) meters per second.
2. Understand that the speed of light \( c \) is a constant in a vacuum, meaning it does not change regardless of the type of light or its properties.
3. Since \( c \) is constant, rearrange the equation to express frequency in terms of wavelength: \[ \nu = \frac{c}{\lambda} \] This shows that frequency is inversely proportional to wavelength.
4. Interpret the inverse proportionality: as the wavelength \( \lambda \) increases, the frequency \( \nu \) must decrease to keep the product \( \nu \times \lambda \) equal to the constant speed of light \( c \). Conversely, if wavelength decreases, frequency increases.
5. Conclude that the correct description of the relationship between frequency and wavelength of light is that they are inversely proportional; as wavelength increases, frequency decreases.