Final answer:
To calculate the bandwidth of the light source in THz, convert the wavelengths to frequencies using the speed of light equation and then find the difference. The bandwidth of a spectrum from 400 nm to 800 nm is 375 THz.
Step-by-step explanation:
The student asked: "If the light source has a rectangle shaped spectrum that starts from 400nm and ends at 800nm, what is the bandwidth of the light source in the unit of THz?" To calculate the bandwidth of the light source in terahertz (THz), you need to convert the given wavelength range into a frequency range and then find the difference between the frequencies.
Steps to calculate the bandwidth in THz:
Use the speed of light equation c = λf, where c is the speed of light (approximately 3 x 10⁸ m/s), λ is the wavelength, and f is the frequency.
Convert the wavelengths from nanometers to meters by multiplying them by 10⁹ (1 nm = 10⁹ m).
Calculate the frequencies for both 400 nm and 800 nm using the speed of light equation.
Convert the frequencies from Hz to THz by dividing them by 10¹.
Subtract the frequency corresponding to 800 nm from the frequency corresponding to 400 nm to find the bandwidth.
Using these steps, let's calculate:
For 400 nm:
λ1 = 400 x 10⁹ m
f1 = c / λ1
f1 = (3 x 10⁸ m/s) / (400 x 10⁹ m)
f1 = 7.5 x 10¹⁴ Hz or 750 THz
For 800 nm:
λ2 = 800 x 10⁹ m
f2 = c / λ2
f2 = (3 x 10⁸ m/s) / (800 x 10⁹ m)
f2 = 3.75 x 10¹⁴ Hz or 375 THz
Bandwidth (THz):
f1 - f2
750 THz - 375 THz
Bandwidth = 375 THz