To determine the correct equation that relates wavelength ([tex]\(\lambda\)[/tex]) and frequency ([tex]\(f\)[/tex]) through the speed of light ([tex]\(c\)[/tex]), let's analyze each of the given options:
A. [tex]\( K E = \frac{1}{2} m v^2 \)[/tex]
- This equation represents the kinetic energy ([tex]\(KE\)[/tex]) of a moving object, where [tex]\(m\)[/tex] is the mass and [tex]\(v\)[/tex] is the velocity. This is not relevant to the relationship involving wavelength, frequency, and the speed of light.
B. [tex]\( c = \lambda f \)[/tex]
- This equation correctly shows the relationship where the speed of light ([tex]\(c\)[/tex]) is the product of its wavelength ([tex]\(\lambda\)[/tex]) and frequency ([tex]\(f\)[/tex]). This is the equation we are looking for.
C. [tex]\( E = h f \)[/tex]
- This equation represents the energy ([tex]\(E\)[/tex]) of a photon, where [tex]\(h\)[/tex] is Planck's constant, and [tex]\(f\)[/tex] is the frequency. While related to frequency, it does not involve the wavelength or speed of light directly in the context the question is asking.
D. [tex]\( f = c \lambda \)[/tex]
- This equation is incorrect. It incorrectly suggests that frequency is the product of the speed of light and wavelength, which is not accurate.
Among the given choices, the correct equation that accurately relates wavelength and frequency through the speed of light is:
B. [tex]\( c = \lambda f \)[/tex]
Therefore, the correct answer is B.
