Visible light consists of electromagnetic waves with wavelengths (in air) in the range 400–700 nm. The speed of light in air is 3.0 × 108 m/s. What are the frequencies of visible light?

To find the frequencies of visible light, we can use the formula for the speed of light, which is c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.

First, we need to convert the wavelengths from nanometers to meters because the speed of light is given in meters per second.

1 nanometer (nm) = 1 × 10^-9 meters (m)

So, the range of wavelengths for visible light in meters is 400 nm to 700 nm, which is 400 × 10^-9 m to 700 × 10^-9 m, or 4 × 10^-7 m to 7 × 10^-7 m.

Next, we rearrange the formula for the speed of light to solve for frequency: ν = c / λ.

For the shortest wavelength (4 × 10^-7 m), the frequency is:

ν = (3.0 × 10^8 m/s) / (4 × 10^-7 m) = 7.5 × 10^14 Hz

For the longest wavelength (7 × 10^-7 m), the frequency is:

ν = (3.0 × 10^8 m/s) / (7 × 10^-7 m) = 4.29 × 10^14 Hz

So, the frequencies of visible light range from about 4.29 × 10^14 Hz to 7.5 × 10^14 Hz.