In 1817, Thomas Young, in correspondence with François Arago, proposed a radical hypothesis: light waves oscillate perpendicular (transverse) to their direction of propagation, rather than parallel (longitudinal) like sound waves.

Mathematical Transverse Wave Field Vector¶

For a plane light wave propagating along the $z$-axis with wave vector $\mathbf{k} = k \hat{\mathbf{z}}$, the electric field vector $\mathbf{E}$ satisfies:

$$\mathbf{k} \cdot \mathbf{E} = 0 \implies E_z = 0$$

$$\mathbf{E}(z,t) = E_x \cos(kz - \omega t) \hat{\mathbf{i}} + E_y \cos(kz - \omega t + \phi) \hat{\mathbf{j}}$$

Resolution of Polarization Anomalies¶

• Explained why light exhibits polarization states ($|H\rangle, |V\rangle$) while acoustic waves do not.

• Explained double refraction in calcite and complete extinction through crossed polarizers.

• Formed the essential foundation for Maxwell’s electromagnetic wave theory ($\nabla \cdot \mathbf{E} = 0$).