Answer to Question #117320 in Optics for shreevathsa BK

Question

With a laser, fringes remain clearly visible, when the path difference was increased up to X m, Deduce Coherence time and spectral half width given λ = 11.5x10-7 m.
X = 1.768 T = 77323

Answer 1

As per the question,

Wavelength of the laser beam $(\lambda)=11.5\times 10^{-7}m$

Speed of light $(c)=3\times 10^8 m/sec$

$l_{coh}=1.768m$

$t_{coh}=\dfrac{l_{coh}}{c}=\dfrac{1.768}{3\times 10^{8}}sec=5.9\times 10^{-9}=5.9ns$

$\Delta \lambda=\dfrac{\lambda^2}{l}=\dfrac{(11.5\times 10^{-7})^2}{1.768}=74.8\times 10^{-14}m=7.48\times 10^{-15}m$