In an interference, the intensity of two interfering waves are I and 4I respectively. They produce intensity at two points A and B with phase angle of π/2 and π respectively. Then difference in between them is

Question

In an interference, the intensity of two interfering waves are I and 4I respectively. They produce intensity at two points A and B with phase angle of π/2 and π respectively. Then difference in between them is (A) I (B) 2I (C) 4I (D) 5I

Tardigrade Admin · Accepted Answer

Resultant intensity, I=I1+I2+2√I1I2cos φ Here, I1=I,I2=4I,φ1=(π/2) and φ2=π At A intensity, IA=I+4I+2√4I2 cos (π/2)=5I At B intensity, IB=I+4I+2√4I2cos π=5I-4I=I Therefore, difference between intensities is IA-IB = 5I-I = 4I

Q. In an interference, the intensity of two interfering waves are I and 4I respectively. They produce intensity at two points A and B with phase angle of π/2 and π respectively. Then difference in between them is

I

2I

4I

5I

Resultant intensity, I=I1​+I2​+2I1​I2​​cosϕ Here, I1​=I,I2​=4I,ϕ1​=2π​ and ϕ2​=π At A intensity, IA​=I+4I+24I2​cos2π​=5I At B intensity, IB​=I+4I+24I2​cosπ=5I−4I=I Therefore, difference between intensities is IA​−IB​=5I−I=4I

Q. In an interference, the intensity of two interfering waves are $I$ and $4 I$ respectively. They produce intensity at two points A and B with phase angle of $π$ /2 and $π$ respectively. Then difference in between them is