Question

Young's double slit experiment is performed using light of wave length $\lambda$. One of the slits is covered by a thin glass sheet of refractive index $\mu$ at this wavelength. The smallest thickness of the sheet to bring the adjacent minimum to the centre of the screen is

• A. $\frac{\lambda }{2(\mu -1)}$
  
• B. $\frac{\lambda }{(\mu -1)}$
  
• C. $\frac{\lambda }{2\mu }$
  
• D. $\frac{\lambda }{\mu }$

Answer 1

The correct option is A $\frac{\lambda }{2(\mu -1)}$


To bring the adjacent minimum to the centre of the screen, the path created by the slit shuould be equal to $\frac{\lambda }{2}$. The path difference created by a sheet of thickness 't' and refractive index $\mu$ is given by $(\mu -1)t$.
Hence, $\frac{\lambda }{2}$ = $(\mu -1)t$ and $t=\frac{\lambda }{2(\mu -1)}$