Question

calculate the coherence time and coherence length of white light of wave length range of 3500 angstrom to 6500 angstrom

Answer 1

As per the given question,

The range of the wavelengths of the lights are

$\lambda_1=3500 A^\circ = 3500\times 10^{-10}m$

$\lambda_2=6500 A^\circ = 6500\times 10^{-10}m$

We know that,

$T=\frac{\lambda}{c}$

Hence,

$\Rightarrow T_1=\frac{3500\times 10^{-10}}{3\times 10^8}sec =1166.67\times 10^{-18}s$

$\Rightarrow T_1 = 1.167\times 10^{-15}s$

$T_2=\frac{6500\times 10^{-10}}{3\times 10^8}sec =2.167\times10^{-15}s$

Hence coherence time $(\Delta T) = (2.167\times 10^{-15}-1.167\times 10^{-15})$

$=1\times 10^{-15}sec$

coherence length $(l)=c\times \Delta T$

$\Rightarrow l=3\times 10^{8}\times10^{-15}m$

$\Rightarrow l = 3\times 10^{-7}m$