The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be :

CONCEPT:

• The intensity is directly proportional to the square of the amplitude and it is written as;

            I ∝ A²

           Here we have "I" as the intensity and A as the amplitude.

• The resultant intensity is written as:

           I = \({I_1+I_2+2\sqrt {I_1I_2}cos ϕ}\)

          Here we have I₁, I₂ are the intensities of two beams, and ϕ is the phase difference.

CALCULATION:

Given:

The intensity of the first beam, I₁ = I

The intensity of the second beam, I₂ = 9I

The phase difference at point P = π/2 

and the phase difference at point Q = π 

Now, the resultant intensity at point P with a phase difference π/2,

I_p = \({I+9I+2\sqrt {I\times 9I}cos \frac{π}{2}}\)

Ip = 10I

⇒ I_p = 10I

Now, the resultant intensity at point P with a phase difference π, 

I_q = \({I+9I+2\sqrt {I\times 9I}cos{π}}\)

I_q = 10I - 6I

⇒ Iq = 4I

Now, the difference in the intensity of beam P and Q we have;

I = I_p - I_q

⇒ I = 10I - 4I

⇒ I = 6I

Hence option 2) is the correct answer.