Q 12-08-222JEE MainJEE Main 2018 (15 Apr, Shift 2)Medium
A plane polarized monochromatic EM wave is travelling in vacuum along $z$ direction such that at $t = t_1$ it is found that the electric field is zero at a spatial point $z_1$. The next zero that occurs in its neighbourhood is at $z_2$. The frequency of the electromagnetic wave is:
Answer: (C) $\dfrac{1.5\times10^8}{|z_2 - z_1|}$
At a given instant, successive zeros of $E = E_0\sin(kz - \omega t)$ are half a wavelength apart:
$$|z_2 - z_1| = \frac\lambda2 \quad\Rightarrow\quad \lambda = 2|z_2 - z_1|$$
$$\nu = \frac{c}{\lambda} = \frac{3\times10^8}{2|z_2 - z_1|} = \frac{1.5\times10^8}{|z_2 - z_1|}$$
Solution by Sreeraj P, M.Sc Physics