Electromagnetic Waves

Step: Find the speed of the wavefront in the medium. 
The wavefront has two parts, one reaches at \(A\) and other reaches at point \(B\) form point \(C\) as shown in the figure.
    
By using trigonometry \(CB = AB ~\text{sin 30}^{\circ} = \frac{L}{2}. \)
The speed of the wavefront in the medium is given by \(\frac{\text{distance}}{\text{time}} =\frac{L}{2T}.\)
Hence, option (3) is the correct answer.

Hint: The net electric field is given by, \(E=\sqrt{{E_1}^2+{E_2}^2+2E_1E_2cos\theta }\).

Step 1: Find the net electric field.
\(\vec{E}=E_{0}[\hat{\imath} \cos (\omega t-k z)+\hat{\jmath} \cos (\omega t-k x)]\)
\(\vec{E_1}=E_{0}\hat{\imath} \cos (\omega t-k z)\)
\(\vec{E_2}=E_{0}\hat{\jmath} \cos (\omega t-k x)\)
The angle between E₁ and E₂ = 90^o
\(E=\sqrt{{E}^2+{E}^2}=\sqrt2 E\)