Q44. The intensity of light due to (see figure) interference of two waves (1) and (2) which have pat

Q: What is the correct answer for CUET UG Physics Q44?

The correct answer is D. In interference, when two coherent waves of individual intensity I₀ interfere, the resultant intensity (I) at a point depends on the phase difference (φ) between them. The general formula for the resultant intensity is I = I₁ + I₂ + 2√(I₁I₂) cos φ. Given that the intensity of each wave is I₀, so I₁ = I₂ = I₀. Therefore, I = I₀ + I₀ + 2√(I₀ * I₀) cos φ = 2I₀ + 2I₀ cos φ = 2I₀ (1 + cos φ). Using t

Q: Q44. The intensity of light due to (see figure) interference of two waves (1) and (2) which have path difference of Δ is: (where I₀ = Intensity of each wave) S P (1) S (2) S Screen (a) Zero (b)…

The correct answer is D. In interference, when two coherent waves of individual intensity I₀ interfere, the resultant intensity (I) at a point depends on the phase difference (φ) between them. The general formula for the resultant intensity is I = I₁ + I₂ + 2√(I₁I₂) cos φ. Given that the intensity of each wave is I₀, so I₁ = I₂ = I₀. Therefore, I = I₀ + I₀ + 2√(I₀ * I₀) cos φ = 2I₀ + 2I₀ cos φ = 2I₀ (1 + cos φ). Using t

Q: What are the options for this CUET UG Physics question?

A. Zero · B. I₀ · C. 2I₀ · D. 4I₀

Question

Q44. The intensity of light due to (see figure) interference of two waves (1) and (2) which have path difference of Δ is: (where I₀ = Intensity of each wave)
S
P
(1)
S
(2)
S
Screen
(a) Zero
(b) Io
(c) 210
(d) 41o

FirstInTest · Accepted Answer

In interference, when two coherent waves of individual intensity I₀ interfere, the resultant intensity (I) at a point depends on the phase difference (φ) between them. The general formula for the resultant intensity is I = I₁ + I₂ + 2√(I₁I₂) cos φ. Given that the intensity of each wave is I₀, so I₁ = I₂ = I₀. 
Therefore, I = I₀ + I₀ + 2√(I₀ * I₀) cos φ = 2I₀ + 2I₀ cos φ = 2I₀ (1 + cos φ). 
Using the trigonometric identity 1 + cos φ = 2 cos²(φ/2), the formula becomes I = 2I₀ (2 cos²(φ/2)) = 4I₀ cos²(φ/2). 
The phase difference (φ) is related to the path difference (Δ) by φ = (2π/λ)Δ. 
So, I = 4I₀ cos²(πΔ/λ). 
If the interference is constructive (e.g., at the central maximum), the path difference Δ = nλ (where n is an integer), which means φ = 2nπ. In this case, cos²(φ/2) = cos²(nπ) = 1. Therefore, the maximum intensity is I_max = 4I₀. The options provided are numerical multiples of I₀, implying the question asks for the maximum possible intensity in constructive interference. Thus, 4I₀ is the correct answer. The solution S44 shows the calculation for Δ = λ, which leads to I = 4I₀.

Answer

Zero

Answer

I₀

Answer

2I₀

Answer

4I₀

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