Two plane polarized light waves combine at a certain point whose electric field components are $E_1=E_0 \sin \omega t$ and $E_2=E_0 \sin \left(\omega t+\frac{\pi}{3}\right)$. Find the amplitude of the resultant wave.

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Wave Optics

Two plane polarized 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 + \frac{π}{3})

. Find the amplitude of the resultant wave.

(A) $0.9 E_{0}$
(B) $E_{0}$
(C) $1.7 E_{0}$ ✓ Correct
(D) $3.4 E_{0}$

Answer: (C)

Solution

Two waves of equal amplitude

E_{0}

with phase difference

δ = \frac{π}{3}

combine to give a resultant amplitude

E = E_{0}^{2} + E_{0}^{2} + 2 E_{0}^{2} cos \frac{π}{3} = 2 E_{0}^{2} + E_{0}^{2} = 3 E_{0} .

Numerically this is about

1.7 E_{0}

.
The amplitude of the resultant wave is

3 E_{0} \approx 1.7 E_{0}

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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