What equation is used to relate wavelength and frequency through the speed of light? \[ f=c \lambda \] \( E=h f \) \( K E=1 / 2 m v^{2} \) \( c=\lambda f \)

The equation that relates **wavelength** (\( \lambda \)) and **frequency** (\( f \)) through the **speed of light** (\( c \)) is: \[ c = \lambda f \] ### Explanation: - **\( c \)**: Speed of light in a vacuum, approximately \( 3 \times 10^8 \) meters per second (m/s). - **\( \lambda \)**: Wavelength, the distance between successive peaks of a wave, measured in meters (m). - **\( f \)**: Frequency, the number of waves that pass a given point per second, measured in hertz (Hz). This equation shows that the speed of light is equal to the product of its wavelength and frequency. If you know any two of these quantities, you can solve for the third. ### Incorrect Options Explained: 1. **\( f = c \lambda \)** - **Incorrect**: This incorrectly suggests that frequency is the product of speed and wavelength. Dimensionally, frequency has units of \( \text{Hz} \) (s\(^{-1}\)), while \( c \lambda \) has units of m\(^2\)/s, which do not match. 2. **\( E = h f \)** - **Incorrect in this context**: This is the equation for the energy (\( E \)) of a photon, where \( h \) is Planck's constant. While it relates energy and frequency, it does not directly relate wavelength and speed of light. 3. **\( KE = \frac{1}{2} m v^{2} \)** - **Incorrect**: This is the classical formula for kinetic energy (\( KE \)) of an object with mass (\( m \)) and velocity (\( v \)). It is unrelated to the relationship between wavelength, frequency, and the speed of light. ### Summary: To relate wavelength and frequency through the speed of light, use: \[ c = \lambda f \] This fundamental relationship is essential in various fields of physics, including optics, telecommunications, and quantum mechanics.