To determine the smallest time delay that can give rise to observable destructive interference between 600 nm monochromatic light beams in an interferometer, we need to consider the conditions for destructive interference.
Destructive interference occurs when two coherent waves have a path length difference that is an odd multiple of half the wavelength. In an interferometer, this path length difference can be created by introducing a time delay between the two beams.
The formula for the path length difference (Δx) in terms of time delay (Δt) and the speed of light (c) is given by:
Δx = c * Δt
To find the minimum time delay, we can set the path length difference equal to half the wavelength (λ/2):
Δx = λ/2
Substituting the values, we have:
c * Δt = λ/2
Δt = λ / (2c)
Now, we can calculate the smallest time delay:
λ = 600 nm = 600 x 10^(-9) m (converting from nanometers to meters) c = speed of light = 299,792,458 m/s
Δt = (600 x 10^(-9) m) / (2 * 299,792,458 m/s)
Δt ≈ 1 x 10^(-15) s
Therefore, the smallest time delay that can give rise to observable destructive interference between 600 nm monochromatic light beams in an interferometer with the same path lengths is approximately 1 femtosecond (1 fs).