Question

Two coherent beams of wavelength $5000 \, \overset{^\circ }{A}$ reaching a point would individually produce intensities $1.44$ and $4.00$ units. If they reach there together, the intensity is $10.24$ units. Calculate the lowest phase difference with which the beams reach that point.

• A. $zero$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi $

Answer 1

Answer: (A)

Resultant intensity at the point where the two coherent beam reach together is given by
$I=I_{1}+I_{2}+2\sqrt{I_{1} \, I_{2}}cos \phi$
$\Rightarrow \, \, \, 10.24=1.44+4.00+2 \, \sqrt{1.44 \times 4.00}cos \phi$
$\Rightarrow \, 10.24=5.44+4.8cos \phi$
$\Rightarrow \, cos \phi=\frac{10.24 - 5.44}{4.8}=1$
$\Rightarrow \, \, \, \phi=0$