Question

If wave length changes by $\Delta \lambda$ then change in magnitude of propagation vector is

• A. $\Delta k$
• B. $2\pi \Delta \lambda$
• C. $\frac{2\pi }{\lambda }\Delta \lambda$
• D. $\frac{2\pi }{{\lambda }^2}\Delta \lambda$

Answer 1

Answer: (D)

$\frac{2\pi }{{\lambda }^2}\Delta \lambda$

$K=\frac{2\pi }{\lambda }$
differentiating both sides, $\Rightarrow \partial k=-\frac{2\pi }{{\lambda }^2}\partial \lambda$
$\therefore \Delta K=\frac{2\pi }{{\lambda }^2}\Delta \lambda$