A plane polarized monochromatic EM wave is travelling a 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:

A plane polarized monochromatic EM wave travels along the z-direction. At time $$t = t_1$$, the electric field is zero at point $$z_1$$, and the next zero in its neighbourhood is at $$z_2$$.

The electric field of a sinusoidal plane wave can be written as $$E = E_0 \sin(kz - \omega t)$$. At a fixed time $$t = t_1$$, this becomes $$E = E_0 \sin(kz - \omega t_1)$$.

The zeros of $$\sin(kz - \omega t_1)$$ occur when $$kz - \omega t_1 = n\pi$$ for integer $$n$$. Two consecutive zeros are separated by $$k(z_2 - z_1) = \pi$$, giving $$|z_2 - z_1| = \frac{\pi}{k} = \frac{\lambda}{2}$$.

Therefore the wavelength is $$\lambda = 2|z_2 - z_1|$$.

Using the relation $$f = \frac{c}{\lambda}$$ where $$c = 3 \times 10^8$$ m/s: $$f = \frac{3 \times 10^8}{2|z_2 - z_1|} = \frac{1.5 \times 10^8}{|z_2 - z_1|}$$.

The correct answer is Option C: $$\frac{1.5 \times 10^8}{|z_2 - z_1|}$$.