Question

Interference fringes are produced on a screen by using two light sources of intensities 'I' and '9I'. The phase difference between the beams is $\frac{\pi }{2}$ at point P and $\pi$ at point Q on the screen. The difference between the resultant intensities at point P and Q is :

• A. $2I$
• B. $4I$
• C. $6I$
• D. $8I$

Answer 1

The correct option is C $6I$

Given : $I_1=I$ $I_2=9I$

Resultant intensity at a point $I^{\prime }=I_1+I_2+2\sqrt{I_1{I}_2}\cos \delta$

At point P : $\delta =\pi /2$

Resultant intensity at P, $I_P^{\prime }=I+9I+2\sqrt{\left(I\right)\left(9I\right)}\cos \left(\pi /2\right)$

Or $I_P^{\prime }=I+9I+6I\times 0=10I$

At point Q : $\delta =\pi$

Resultant intensity at Q, $I_Q^{\prime }=I+9I+2\sqrt{\left(I\right)\left(9I\right)}\cos \left(\pi \right)$

Or $I_P^{\prime }=I+9I-6I=4I$

Thus difference in resultant intensities $I_P^{\prime }-I_Q^{\prime }=10I-4I=6I$