JEE Advanced · 2009 · 12 Apr 2009 · Paper 2 · Wave Optics

Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$. In each of these cases ${\mathrm{S}}_1{\mathrm{P}}_0={\mathrm{S}}_2{\mathrm{P}}_0,{\mathrm{S}}_1{\mathrm{P}}_1-{\mathrm{S}}_2{\mathrm{P}}_1=\lambda /4$ and ${\mathrm{S}}_1{\mathrm{P}}_2-{\mathrm{S}}_2{\mathrm{P}}_2=\lambda /3$, where $\lambda$ is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index $\mu$ and thickness $t$ is pasted on slit ${\mathrm{S}}_2$. The thicknesses of the sheets are different in different cases. The phase difference between the light waves reaching a point P on the screen from the two slits is denoted by $\delta (\mathrm{P})$ and the intensity by $I(\mathrm{P})$. Match each situation given in Column I with the statement(s) in Column II valid for that situation.

Column I
(A) (see structure)
(B) $(\mu -1)t=\lambda /4$ (see structure)
(C) $(\mu -1)t=\lambda /2$ (see structure)
(D) $(\mu -1)t=3\lambda /4$ (see structure)

Column II
(p) $\delta \left({\mathrm{P}}_0\right)=0$
(q) $\delta \left({\mathrm{P}}_1\right)=0$
(r) $I\left({\mathrm{P}}_1\right)=0$
(s) $I\left({\mathrm{P}}_0\right)>I\left({\mathrm{P}}_1\right)$
(t) $I\left({\mathrm{P}}_2\right)>I\left({\mathrm{P}}_1\right)$