Question

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is π. The difference of resultant intensities, at the point A and B, will be_______I.

Answer 1

Correct Answer: 24

To solve the problem, we need to evaluate the resultant intensities at points A and B where two light beams interfere. The given intensities are 4I and 9I; these represent the intensities of the individual light beams.

Step 1: Calculate Resultant Intensity at Point A 
At point A, the phase difference ϕ = 0, meaning the waves are in phase. The formula for resultant intensity I_res when two coherent beams interfere is: I_res = I₁ + I₂ + 2√(I₁ I₂) cos ϕ.
Substituting I₁ = 4I, I₂ = 9I, and cos(ϕ) = cos(0) = 1:
I_res,A = 4I + 9I + 2√(4I * 9I)
= 13I + 12I = 25I.

Step 2: Calculate Resultant Intensity at Point B
At point B, the phase difference ϕ = π, meaning the waves are out of phase. Use the same formula but with cos(ϕ) = cos(π) = -1:
I_res,B = 4I + 9I + 2√(4I * 9I) * (-1)
= 13I - 12I = 1I.

Step 3: Determine the Difference of Resultant Intensities
The difference between the intensities at points A and B is:
ΔI = I_res,A - I_res,B = 25I - 1I = 24I.

The computed intensity difference ΔI = 24I fits within the expected range of 24,24. Hence, the difference of resultant intensities, at points A and B, is 24I.

Answer 2

\(I_A = (\sqrt{I_1} + \sqrt{I_2})^2 = 25I\)
\(I_B = (\sqrt{I_1} - \sqrt{I_2})^2 = I\)
So,\(I_A - I_B = 25I - I\)
\(= 24I\)
So, the answer is 24.