Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is 0° and in other case is π /2, the ratio of the intensities in the two cases will be

Question

Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is 0° and in other case is π /2, the ratio of the intensities in the two cases will be (A) 1: 1 (B) 2: 1 (C) 4: 1 (D) none of these

Tardigrade Admin · Accepted Answer

From IR=I1+I2+2√I1I2 cosφ When φ=0Â°, IR=I+I+2√II cos0Â°=4I When φ=90Â°, I 'R=I+I+2√II cos90Â°=2I ∴ (IR/I 'R)=(4I/2I)=2: 1

Q. Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is $0^{°}$ and in other case is $π /2$ , the ratio of the intensities in the two cases will be

$1 : 1$

$2 : 1$

$4 : 1$

none of these

From $I_{R} = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
When $ϕ = 0^{°}, I_{R} = I + I + 2 II cos 0^{°} = 4 I$
When $ϕ = 9 0^{°}, I_{R}^{'} = I + I + 2 II cos 9 0^{°} = 2 I$
$∴ \frac{I _{R}}{I _{R}^{'}} = \frac{4 I}{2 I} = 2 : 1$

Q. Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is 0° and in other case is π/2, the ratio of the intensities in the two cases will be

1:1

2:1

4:1