Question

White light is incident normally on a glass plate of thickness $0.50\times {10}^{-6}m$ and index of refraction $1.50$ . Which wavelengths in the visible region $400nm-700nm$ are strongly reflected by the plate?

• A. $429nm$
• B. $600nm$
• C. $481nm$
• D. $576nm$

Answer 1

Answer: (A), (B)

The correct options are
A $429nm$
B $600nm$

The light of wavelength $\lambda$ is strongly reflected if $2\mu d=\left(n+\frac{1}{2}\right)\lambda$----- (i)
where n is a non negitive integr.
Here $2\mu d=2\times 1.50\times 0.5\times {10}^{-6}m=1.5\times {10}^{-6}m$
Putting $\begin{array}{c}\lambda =400\mathrm{nm}\text{in Eq.}\left(i\right),\text{we get}\\ 1.5\times {10}^{6}m=\left(n+\frac{1}{2}\right)\left(400\times {10}^{-9}m\right)\\ \Rightarrow n=3.25\end{array}$

putting $\lambda =700nm$ in Eq. (i),
we get
$1.5\times {10}^{-6}m=(n+\frac{1}{2}(700\times {10}^{-9}m$
$⟹n=1.66$
Thus, within $400nm$ to $700nm$, the integer $n$ can take the values $2$ and $3$. Putting these values of $n$ in E.q (i), the wavelengths become $\lambda =\frac{4\mu d}{2n+1}=600nm$ and $429nm$.

Thus, light of wavelengths $429nm\text{and}600nm$ are strongly reflected.