Two plane waves having amplitude $E_0$ are described by $\vec{E}_1=E_0 \cos \left(\overrightarrow{k_1} \cdot \vec{r}-\omega t\right) \hat{z}$ and $\vec{E}_2=E_0 \cos \left(\vec{k}_2 \cdot \vec{r}-\omega t\right) \hat{z}$. The wavevectors $\vec{k}_1$ and $\vec{k}_2$ pass through the origin making an angle of $45^{\circ}$ with $x$-axis, as shown in the figure. At $t=0$ and $x=0$ plane, the correct option(s) is(are)

• Correct answer
  A

  the periodicity of interfence pattern in the $y z$ plane is $\sqrt{2} \lambda$.
• Correct answer
  B

  the amplitude of resultant wave is $2 E_0$.
• C

  the direction of polarization of resultant wave will change.
• D

  the maximum intensity is $E_0^2$.

Hence, the correct answer is options: 'A', 'B'.