Question

Two plane polarised light waves combine at a certain point whose electric field components are \(E_{1}=E_{0}\sin \omega t\) and \(E_{2}=E_{0}\sin (\omega t+\pi /3)\). The amplitude of the resultant wave is (\(\cos 60^{\circ }=0.5\))

• A. \(3E_{0}\)
• B. \(\sqrt{3}E_{0}\)
• C. \(E_{0}\)
• D. \(E_{0}/\sqrt{3}\)

Hint:

Find the phase difference between the two waves and use the formula for the amplitude of the resultant of two equal amplitude waves.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Two waves of equal amplitude \(E_0\) combine with a phase difference \(\phi\). The resultant amplitude is \(E=\sqrt{E_1^2+E_2^2+2E_1E_2\cos\phi}\).

Step 2: Identify the Data
\(E_1=E_2=E_0\) and the phase difference is \(\phi=\dfrac{\pi}{3}=60^{\circ}\).

Step 3: Calculation
\(E=\sqrt{E_0^2+E_0^2+2E_0^2\cos60^{\circ}}=E_0\sqrt{2+2\times0.5}\)
\(E=E_0\sqrt{3}\)

Step 4: Compare the options
The result \(\sqrt{3}E_0\) matches option (B).

Final Answer:
The amplitude of the resultant wave is \(\sqrt{3}E_0\). \[ \boxed{\text{(B) }\sqrt{3}E_{0}} \]