Two light waves superimposing at the mid-point of the screen are coming from coherent sources of light with phase difference 3p rad. Their amplitudes are 1 cm each. The resultant amplitude at the given point will be,

Question

Two light waves superimposing at the mid-point of the screen are coming from coherent sources of light with phase difference 3p rad. Their amplitudes are 1 cm each. The resultant amplitude at the given point will be, (A) 5 cm (B) 3 cm (C) 2 cm (D) zero

Tardigrade Admin · Accepted Answer

Resultant amplitude, A = √A12 +A22 + 2A1A2 cos φ Here, A1 = A2 = 1 cm, φ = 3π rad ∴ A = √12+12+2× 1× 1× cos 3π = √2+2×(-1) = 0

Q. Two light waves superimposing at the mid-point of the screen are coming from coherent sources of light with phase difference $3 p$ rad. Their amplitudes are $1 c m$ each. The resultant amplitude at the given point will be,

$5 c m$

$3 c m$

$2 c m$

zero

Resultant amplitude,
$A = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos ϕ$
Here, $A_{1} = A_{2} = 1 c m, ϕ = 3 π r a d$
$∴ A = 1^{2} + 1^{2} + 2 \times 1 \times 1 \times cos 3 π$
$= 2 + 2 \times (- 1) = 0$

Q. Two light waves superimposing at the mid-point of the screen are coming from coherent sources of light with phase difference 3p rad. Their amplitudes are 1cm each. The resultant amplitude at the given point will be,

5cm

3cm

2cm