Coherence length and coherence time of light

[Supertramp19]

Homework Statement

Monochromatic light (λ = 500 nm) from a particular light source has a frequency
bandwidth Δν = 6 x 1011 Hz.

(a) What is the coherence length Δx and the coherence time Δt of this light?
(b) What is approximately the largest optical path length difference in an
interference experiment with this light, which would still give you observable
interference fringes? Make a sketch of such an experiment.

Homework Equations

Coherence length: Δx= cΔt
Δt=1/Δv
Path Difference: Δ=mλ=asinθ

The Attempt at a Solution

So, I figured out that Δx=5*10^-4 m and Δt=1.66*10^-12 s. I don't really know how to use these to find the largest optical path length. I have the equation, λ... What else do I need to figure out. Would I be using Young's Double Slit Experiment? Thanks for the help. :)

 

[lanedance]

Homework Statement

Monochromatic light (λ = 500 nm) from a particular light source has a frequency
bandwidth Δν = 6 x 1011 Hz.

(a) What is the coherence length Δx and the coherence time Δt of this light?
(b) What is approximately the largest optical path length difference in an
interference experiment with this light, which would still give you observable
interference fringes? Make a sketch of such an experiment.

Homework Equations

Coherence length: Δx= cΔt
Δt=1/Δv
Path Difference: Δ=mλ=asinθ

The Attempt at a Solution

So, I figured out that Δx=5*10^-4 m and Δt=1.66*10^-12 s. I don't really know how to use these to find the largest optical path length. I have the equation, λ... What else do I need to figure out. Would I be using Young's Double Slit Experiment? Thanks for the help. :)

I don't think your numbers line up with the equations you've given... looks like a simple error, but i would check them, shouldn't you calculate Δt first?

for the second part, think about splitting the beam of light in two then recombining... what do think will happen if the path length is greater than the coherence length

Though it could apply , I don't think Young's double slit experiment is the best answer here, as it requires the light through each slit is coherent with each other, which happpens by having the same source for both slits, though the effect is probably more noticeable with the limited frequency content.