Two plane polarised light waves combine at a certain point whose electric field component are , . Find the amplitude of the resultant wave. [2025]

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Solution

Q.
Two plane polarised light waves combine at a certain point whose electric field component are $E_{1} = E_{0} \sin ω t$ , $E_{2} = E_{0} \sin (ω t + \frac{π}{3})$ . Find the amplitude of the resultant wave. [2025]

1 $0.9 E_{0}$

2 $3.4 E_{0}$

3 $1.7 E_{0}$

4 $0.5 E_{0}$

Ans.
(3)

$E_{1} = E_{0} \sin (ω t)$

$E_{2} = E_{0} \sin (ω t + \frac{π}{3})$

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

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

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

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

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