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?
(a) To find the length of a pulse of light, we can use the formula:
Length of pulse = Speed of light x Time
Given that the pulse lasts 6.2 femtoseconds (fs), we can substitute the values into the formula:
Length of pulse = Speed of light x 6.2 fs
The speed of light is approximately 299,792,458 meters per second (m/s).
Length of pulse = 299,792,458 m/s x 6.2 fs
To convert femtoseconds to seconds, we divide by 1,000,000,000,000 (since there are 1 trillion femtoseconds in a second).
Length of pulse = 299,792,458 m/s x (6.2 fs / 1,000,000,000,000 s/fs)
Calculating the length of the pulse:
Length of pulse = 1.857410546 m
Therefore, the length of a pulse of red light that lasts 6.2 fs is approximately 1.857 meters.
(b) To determine 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 red light.
Number of wavelengths = Length of pulse / Wavelength
Converting the wavelength from nanometers to meters:
Wavelength = 680 nm = 680 x 10^(-9) m
Number of wavelengths = 1.857 m / (680 x 10^(-9) m)
Calculating the number of wavelengths included in the pulse:
Number of wavelengths ≈ 2,731,764.71
Therefore, there are approximately 2,731,764 wavelengths of red light (λ = 680 nm) included in a pulse that lasts 6.2 fs.
To answer these questions, we need to understand the relationship between the duration of a pulse of light and the speed of light.
(a) To find the length of a pulse of red light that lasts 6.2 femtoseconds (fs), we can use the equation:
Length = Speed × Time
Since the speed of light is constant at approximately 3.00 × 10^8 meters per second (m/s), we can substitute this value into the equation:
Length = 3.00 × 10^8 m/s × 6.2 × 10^(-15) s
Multiply the values:
Length = 1.86 × 10^(-6) meters
Therefore, the length of the pulse of red light that lasts 6.2 fs is 1.86 × 10^(-6) meters.
(b) To determine the number of wavelengths of red light included in the pulse, we can use the formula:
Number of Wavelengths = Length / Wavelength
Given that the wavelength of red light (λ) is 680 nm (or 680 × 10^(-9) meters), we can substitute the values into the formula:
Number of Wavelengths = (1.86 × 10^(-6) m) / (680 × 10^(-9) m)
Divide the values:
Number of Wavelengths ≈ 2735
Therefore, there are approximately 2735 wavelengths of red light included in a pulse that lasts 6.2 fs.