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Physics Question 36 – JEE-MAIN 2026

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In interference experiment the path difference between two interfering waves at a point A on the screen is λ/3, where λ is the wavelength of these waves, and at another point B the path difference is λ/6. The ratio of intensities at points A and B is _______.

The phase difference is crucial for determining the intensity in an interference pattern.

Step 1: Calculate phase differences for points A and B✦ Active

The phase difference ϕ is related to the path difference Δx by the formula ϕ=2πλΔx.

For point A: ΔxA=λ3⟹ϕA=2πλ(λ3)=2π3
For point B: ΔxB=λ6⟹ϕB=2πλ(λ6)=π3
Step 2: Calculate intensities at points A and B○ Expand

The intensity I at a point in an interference pattern is given by I=Imaxcos2⁡(ϕ2), where Imax is the maximum intensity.

For point A: IA=Imaxcos2⁡(2π/32)=Imaxcos2⁡(π3)=Imax(12)2=Imax4
For point B: IB=Imaxcos2⁡(π/32)=Imaxcos2⁡(π6)=Imax(32)2=3Imax4
Step 3: Determine the ratio of intensities IA/IB○ Expand

Now, we find the ratio of the intensities IA to IB.

IAIB=Imax/43Imax/4=13
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