Two plane polarized light waves combine at a certain point whose electric field components are E 1 =E 0 Sin ω t E 2 =E 0 Sin (ω t+π/3 ) Find the amplitude of the resultant wave.

Physics · Wave Optics

JEE Main 2025 — 7 April, Morning Shift — Question 50

Two plane polarized light waves combine at a certain point whose electric field components are

$E_{1}=E_{0} \operatorname{Sin} \omega t$ $E_{2}=E_{0} \operatorname{Sin}\left(\omega t+\frac{\pi}{3}\right)$ Find the amplitude of the resultant wave.

Option A:
$1.7 E_{0}$
Correct
Option B:
$0.9 E_{0}$
Option C:
$E_{0}$
Option D:
$3.4 E_{0}$

Answer: A

Step-by-step solution

$E_{1}=E_{0} \sin (\omega t)$ $E_{2}=E_{0} \sin \left(\omega t+\frac{\pi}{3}\right)$ $E_{R}^{2}=E_{1}^{2}+E_{2}^{2}+2 E_{1} E_{2} \cos (\phi)$

$E_{R}^{2}=E_{0}^{2}+E_{0}^{2}+2 E_{0}^{2} \cos \phi=2 E_{0}^{2}(1+\cos \phi)$

$E_{R}^{2}=2 E_{0}^{2} \times 2 \cos ^{2}\left(\frac{\pi}{6}\right)=4 E_{0}^{2} \cdot \frac{3}{4}$

Hence, $E_{R}=E_{0} \sqrt{3} \approx 1.7 E_{0}$

Answer key and solution verified before publishing.

Practise Wave Optics

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2025
Paper: 7 April, Morning Shift
Subject: Physics
Chapter: Wave Optics
Topic: Polarization of Light Waves