Two plane polarised light waves combine at a certain point whose electric field components are E 1 = E 0 sin ω t and E 2 = E 0 sin ( ω t + π /3 ) . The amplitude of the resultant wave is ( cos

Question

Two plane polarised light waves combine at a certain point whose electric field components are E 1 ​ = E 0 ​ sin ω t and E 2 ​ = E 0 ​ sin ( ω t + π /3 ) . The amplitude of the resultant wave is ( cos 6 0 ∘ = 0.5 )

TestHub · Accepted Answer

The given electric field components are $E_{1} = E_{0} sin ω t$ and $E_{2} = E_{0} sin (ω t + π /3)$ .

The phase difference between the two waves is $ϕ = π /3 = 6 0^{\circ}$ .

The amplitude of the resultant wave is given by

$E_{R} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos ϕ$

Substituting $A_{1} = E_{0}$ , $A_{2} = E_{0}$ , and $ϕ = 6 0^{\circ}$ :

$E_{R} = E_{0}^{2} + E_{0}^{2} + 2 E_{0}^{2} cos 6 0^{\circ}$

Since $cos 6 0^{\circ} = 0.5$ :

$E_{R} = 2 E_{0}^{2} + 2 E_{0}^{2} (0.5)$

$E_{R} = 2 E_{0}^{2} + E_{0}^{2}$

$E_{R} = 3 E_{0}^{2} = 3 E_{0}$

Answer: $3 E_{0}$

Physics - Wave Optics Question with Solution | TestHub

Options:

Doubts & Discussion