JEE Main 2025 · 7 April · morning · Single correct · +4 / −1
Two plane polarized light waves combine at a certain point whose electric field components are
E₁=E₀ Sin ω t ; E₂=E₀ Sin(ω t+π/3)
Find the amplitude of the resultant wave.
- (a) 1.7 E₀
- (b) E₀
- (c) 0.9 E₀
- (d) 3.4 E₀
Answer and solution
Answer (a) 1.7 E₀
Solution
Physics sir · 4 steps
Same frequency, phase gap of π/3: add them like two vectors at 60°, not like two plain numbers.
- Treat as phasors. Both waves have the same frequency ω and, taken along the same line, superpose into one wave of that frequency. Each is a phasor of length E₀, and the angle between them equals the phase difference φ = π/3, that is 60°.
E_R = √(E₀² + E₀² + 2E₀ E₀ cos φ)
- Put in numbers. With cos 60° = 1/2, the term under the root is E₀² + E₀² + E₀² = 3E₀². So E_R = √3 E₀ ≈ 1.73 E₀.
- Quick check. For two equal amplitudes the formula reduces to E_R = 2E₀cos φ/2 = 2E₀cos 30° = √3 E₀, the same result. It also sits between 0 (opposite phase) and 2E₀ (same phase), as it must.
- So. The resultant amplitude is about 1.7 E₀, which is option (a).
The idea to keep. Two waves of the same frequency add like vectors at an angle equal to their phase difference. For equal amplitudes, E_R = 2E₀cos φ/2, always between 0 and 2E₀.
Answer from the NTA final answer key. Solution by PrepWiser.