<Dd> ∇ 2 f (k ^ ⋅ x − c 0 t) = 1 c 0 2 ∂ 2 ∂ t 2 f (k ^ ⋅ x − c 0 t), (\ displaystyle \ nabla ^ (2) f \ left ((\ hat (\ mathbf (k))) \ cdot \ mathbf (x) - c_ (0) t \ right) = (\ frac (1) ((c_ (0)) ^ (2))) (\ frac (\ partial ^ (2)) (\ partial t ^ (2))) f \ left ((\ hat (\ mathbf (k))) \ cdot \ mathbf (x) - c_ (0) t \ right),) </Dd> <P> for a generic wave traveling in the k ^ (\ displaystyle (\ hat (\ mathbf (k)))) direction . </P> <P> This form will satisfy the wave equation . </P> <Dl> <Dd> ∇ ⋅ E = k ^ ⋅ E 0 f ′ (k ^ ⋅ x − c 0 t) = 0 (\ displaystyle \ nabla \ cdot \ mathbf (E) = (\ hat (\ mathbf (k))) \ cdot \ mathbf (E) _ (0) f' \ left ((\ hat (\ mathbf (k))) \ cdot \ mathbf (x) - c_ (0) t \ right) = 0) </Dd> <Dd> E ⋅ k ^ = 0 (\ displaystyle \ mathbf (E) \ cdot (\ hat (\ mathbf (k))) = 0) </Dd> </Dl>

Light is a wave of electric and magnetic fields