Two beams of light having intensities I and 4I interferer to produce a fringe pattern on screen- The phase difference between the beam is -2 at point A and 2- at point B- Then find out the difference between the resultant intensities at A and B-

Resultant intensity #160; #160; I_r = I_1+I_2+2√(I_1I_2)cosϕ Given : #160; #160; I_1 = I #160; #160; #160; #160; I_2 = 4I At p ...

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Byju's Answer

Standard XII

Physics

Intensity Amplitude Relationship

Two beams of ...

Question

Two beams of light having intensities I and 4I interferer to produce a fringe pattern on screen. The phase difference between the beam is $\frac{π}{2}$ at point A and $2 π$ at point B. Then find out the difference between the resultant intensities at A and B.

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Solution

Resultant intensity $I_{r} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} cos ϕ$
Given : $I_{1} = I$ $I_{2} = 4 I$
At point A : $ϕ = \frac{π}{2}$
$I_{A} = I + 4 I + 2 \sqrt{I (4 I)} cos (π / 2) = 5 I$
At point B : $ϕ = 2 π$
$I_{B} = I + 4 I + 2 \sqrt{I (4 I)} cos (2 π) = 9 I$
Difference in intensities $I_{B} - I_{A} = 9 I - 5 I = 4 I$

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Two beams of light having intensities I and 4I interferer to produce a fringe pattern on screen. The phase difference between the beam is π2 at point A and 2π at point B. Then find out the difference between the resultant intensities at A and B.

Resultant intensity Ir=I1+I2+2√I1I2cosϕGiven : I1=I I2=4IAt point A : ϕ=π2IA=I+4I+2√I(4I)cos(π/2)=5IAt point B : ϕ=2πIB=I+4I+2√I(4I)cos(2π)=9IDifference in intensities IB−IA=9I−5I=4I

Two beams of light having intensities I and 4I interferer to produce a fringe pattern on screen. The phase difference between the beam is $\frac{π}{2}$ at point A and $2 π$ at point B. Then find out the difference between the resultant intensities at A and B.