An electromagnetic wave travels in vacuum at speed c ≈ 3.00×10^8 m/s. If the frequency is 4.0×10^14 Hz, what is the wavelength?

• A. 3.0×10^-7 m
• B. 1.5×10^-6 m
• C. 2.5×10^-7 m
• D. 7.5×10^-7 m

Answer: (D)

Light in vacuum follows the relation c = fλ, where c is the speed of light, f is the frequency, and λ is the wavelength. Plugging in c ≈ 3.00×10^8 m/s and f = 4.00×10^14 Hz gives λ = c/f = (3.00×10^8)/(4.00×10^14) = 0.75×10^-6 m = 7.5×10^-7 m, which is about 750 nm. This wavelength is in the red part of the visible spectrum. If light traveled through a medium with slower speed, the wavelength would be shorter, since the frequency remains unchanged.