Two waves of intensity ratio 1: 9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is I₁ (b) Waves are coherent is I₂ and differ in phase by 60°. If (I₁)/(I₂) = 10/x then x = _________. Numerical answer type. Work it out, then open the answer.

Answer: 13. Take intensities I and 9I. Incoherent: I₁ = I + 9I = 10I Coherent: I₂ = I + 9I + 2√(I· 9I)cos 60° = 10I + 3I = 13I (I₁)/(I₂) = 10/13, so x = 13.

Two waves of intensity ratio 1: 9 cross each other at a point. The… | JEE Main 2024 (31 Jan, Shift 1)

Q52JEE Main 2024 · 31 JAN · SHIFT 1Medium

Superposition, Coherence & Intensity

Two waves of intensity ratio $1 : 9$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent is $I_2$ and differ in phase by $60^\circ$ . If $\frac{I_1}{I_2} = \frac{10}{x}$ then $x =$ _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 13

Take intensities $I$ and $9I$ .
Incoherent: $I_1 = I + 9I = 10I$
Coherent: $I_2 = I + 9I + 2\sqrt{I\cdot 9I}\cos 60^\circ = 10I + 3I = 13I$
$\frac{I_1}{I_2} = \frac{10}{13}$ , so $x = 13$ .

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