Question

Calculate Coherence length of laser beam for
which
the
bandwidth is 3000 Hz​

Answer 1

Explanation:

The coherence length can be used for quantifying the degree of temporal (not spatial!) coherence as the propagation length (and thus propagation time) over which coherence degrades significantly. It is defined as the coherence time times the vacuum velocity of light.

For light with a Lorentzian optical spectrum resulting from a random walk of the optical phase, the coherence length can be calculated as



where Δν is the (full width at half-maximum) linewidth (optical bandwidth). This coherence length is the propagation length after which the magnitude of the coherence function has dropped to the value of 1 / e.

Answer 2

Answer:

The coherence length of the laser beam for which the bandwidth is 3000 Hz​ is 10⁵m.

Explanation:

This is the formula-based question.

The coherence length defines the largest path difference for which interference is possible.

Coherence length is given as,

       $l_T=c\tau_o$           (1)

Where,

lт=Coherence length

τ₀=Coherence time

c=speed of light=3 × 10⁸m/s

To find coherence length we first need to find the coherence time

which is given as,

$\tau_o=\frac{1}{\Delta \nu}$           (2)

Δν=bandwidth of the source

From the question, we have the bandwidth as 3000 Hz​,

So,

$\tau_o=\frac{1}{3000}$             (3)

By putting equation (3) in equation (1) we get;

$l_T=3\times 10^8\times \frac{1}{3000}$

$l_T=10^5m$

Hence, the coherence length of the laser beam for which the bandwidth is 3000 Hz​ is 10⁵m.