Question

In standard Young's double-slit experiment, visible light $\lambda \in \left(350nm\text{, }750nm\right)$ is used in both the slits. Distance between the slits is $2mm$ , and the distance of the screen from the slits is $1m$ . A thin glass slab $\left(\mu =\text{1.5}\right)$ of thickness $6\mu \text{m}$ is placed in front of slit $S_2$ . Which among the following wavelengths is missing at point $P,$ which is directly in front of slit $S_2$ ?(Neglect dispersion of light)

• A. $400nm$
• B. $500nm$
• C. $600nm$
• D. $700nm$

Answer 1

Answer: (A)

Net path difference $=\left(\mu -1\right)\text{t}-\frac{\text{yd}}{\text{D}}$
$=\left(\frac{3}{2}-1\right)6\mu \text{m}-\frac{\left(\text{d}/2\right)\text{d}}{\text{D}}=1\mu \text{m}$
For Destructive interference
$\Delta \text{x}=1\mu \text{m}=\left(2\text{n}+1\right)\frac{\lambda }{2}\Rightarrow \lambda =\frac{2}{\left(2\text{n}+1\right)}\mu \text{m}$
$\lambda =\frac{\text{2000 nm}}{\left(2+1\right)}=\frac{\text{2000}}{3}$ $(n=1)$
$\lambda =\frac{\text{2000 nm}}{\left(4+1\right)}=\frac{\text{2000}}{5}\text{nm}=\text{400 nm}$ $(n=2)$