Final answer:
The problem involves calculating the spectral purity factor, coherence time, and coherence length of the red line of cadmium with a wavelength of 6943 Å and a spectral width of 0.01 Å. The calculations use fundamental spectral analysis formulae, including the use of the speed of light and the relationship between wavelength, frequency, and spectral width.
Step-by-step explanation:
To calculate the spectral purity factor, coherence time, and coherence length for the red line of cadmium with a wavelength of 6943 Å and a spectral width of 0.01 Å, we need to use the principles of spectral analysis and the formulae that describe the relationship between these parameters
Spectral Purity Factor
The spectral purity factor (ν/Δν) is defined as the ratio of the frequency (ν) to the spectral width (Δν). To find ν, we use the equation ν = c/λ, where c is the speed of light (approximately 3 x 108 m/s) and λ is the wavelength. Then, we calculate Δν by using the formula Δν = Δλ × (c/λ2).
Coherence Time and Coherence Length
The coherence time (τc) is found by taking the inverse of the spectral width (τc = 1/Δν), and the coherence length (Lc) is calculated by multiplying the coherence time by the speed of light (Lc = c × τc). To solve the mathematical problem completely, we plug in the given values and perform the necessary calculations to obtain the spectral purity factor, coherence time, and coherence length.