Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi / 2$ and $\pi / 3$ at points A and B respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ______.

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Wave Optics

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are

π /2

and

π /3

at points A and B respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ______.

Answer: 2

Solution

Resultant intensity is

I_{res} = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ

. At point A with

ϕ = π /2

I_{A} = I + 4 I + 2 I \cdot 4 I cos (π /2) = 5 I + 0 = 5 I

. At point B with

ϕ = π /3

I_{B} = I + 4 I + 2 4 I^{2} cos (π /3) = 5 I + 4 I \times (1/2) = 7 I

. The difference

I_{B} - I_{A} = 7 I - 5 I = 2 I

, so

x = 2

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Integer answer

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