Modern lasers can create a pulse of light that lasts only a few femtoseconds.
(a) What is the length of a pulse of red light that lasts 6.2 fs?
(b) How many wavelengths of red light (ë = 680 nm) are included in such a pulse?
To answer these questions, we need to understand the relationship between the speed of light, the wavelength, and the duration (or length) of a pulse.
(a) To find the length of a pulse of red light lasting 6.2 femtoseconds, we need to multiply the speed of light by the time duration.
The speed of light is approximately 299,792,458 meters per second (m/s), which we can round to 3.00 × 10^8 m/s for simplicity.
Given that the pulse duration is 6.2 femtoseconds (fs), we need to convert it to seconds by dividing by 10^15 (since 1 femtosecond = 10^-15 seconds).
So, the length of the pulse is:
Length = Speed of Light × Time Duration
Length = (3.00 × 10^8 m/s) × (6.2 × 10^-15 s)
Length ≈ 1.86 × 10^-6 meters (m)
(b) To calculate the number of wavelengths of red light (λ = 680 nm) included in the pulse, we divide the length of the pulse by the wavelength of the light.
The wavelength of red light is 680 nanometers (nm), which can be converted to meters by dividing by 10^9 (since 1 nanometer = 10^-9 meters).
So, the number of wavelengths included in the pulse is:
Number of Wavelengths = Length of Pulse / Wavelength
Number of Wavelengths = (1.86 × 10^-6 m) / (680 × 10^-9 m)
Number of Wavelengths ≈ 2.74 wavelengths
Therefore,
(a) The length of a pulse of red light that lasts 6.2 fs is approximately 1.86 × 10^-6 meters (m).
(b) Such a pulse includes approximately 2.74 wavelengths of red light.