Question

A light wave of wavelength ${\lambda }_0$ propogates from point $A$ to point $B$. We introduce in its path a glass plate of refractive index $n$ and thickness $l$. The introduction of the plate alters the phase of the plate at $B$ by an angle $\varphi$. If $\lambda$ is the wavelength of light on emerging from the plate , then

• A. $\Delta \varphi =0$
• B. $\Delta \varphi =\frac{2\pi l}{{\lambda }_0}$
• C. $\Delta \varphi =2\pi l(\frac{1}{\lambda }-\frac{1}{{\lambda }_0})$
• D. $\Delta \varphi =\frac{2\pi l}{{\lambda }_0}(n-1)$

Answer 1

Answer: (C), (D)

$\Delta \varphi =\frac{2\pi l}{{\lambda }_0}(n-1)$

When a light wave propogates from points $A$ to $B$, Phase difference between those two points is zero.

After adding the glass plate:

Phase difference in incident light ${\varphi }_i=\frac{2\pi l}{{\lambda }_0}$

Phase difference in emerging light ${\varphi }_f=\frac{2\pi l}{\lambda }$

$\Delta \varphi =2\pi l(\frac{1}{\lambda }-\frac{1}{{\lambda }_0})$

Further by snell's law, $n\lambda ={\lambda }_0\Rightarrow \lambda =\frac{{\lambda }_0}{n}$

Substituting this we get, $\Delta \varphi =\frac{2\pi l}{{\lambda }_0}(n-1)$