A narrow slit $\mathrm{S}$ transmitting light of wavelength $\mathrm{\lambda }$ is placed at a distance $\mathrm{d}$ above a large plane mirror as shown. The light coming directly from the slit

 

and that coming after the reflection interfere at a screen $\mathrm{\Sigma }$ placed at a distance $\mathrm{D}$ from the slit.
(a) What will be the intensity at a point just above the mirror, i.e., just above $\mathrm{O}$?
(b) At what distance from $\mathrm{O}$ does the first maximum occur?

A double slit $S_1-S_2$ is illuminated by a coherent light of wavelength $\lambda .$ The slits are separated by a distance $\mathrm{d}.$ A plane mirror is placed in front of the double slit at a distance ${\mathrm{D}}_1$ from it and a screen $\Sigma$ is placed behind the double slit at a distance $D_2$ from it. The screen $\Sigma$ receives only the light reflected by the mirror. The fringe-width of the interference pattern on the screen is $\frac{\lambda \left(x{D}_1+D_2\right)}{d}$. Find $x$.

White coherent light $(400 \mathrm{nm}-700 \mathrm{nm})$ is sent through the slits of a Young's double-slit experiment. The separation between the slits is $0.5 \mathrm{mm}$ and the screen is $50 \mathrm{cm}$ away from the slits. There is a hole in the screen at a point $1.0 \mathrm{mm}$ away (along the width of the fringes) from the central line.
(a) Which wavelength(s) will be absent in the light coming from the hole?
(b) Which wavelength(s) will have a strong intensity?

Consider the arrangement shown. The distance $\mathrm{D}$ is large compared to the separation $\mathrm{d}$ between the slits.

(a) The minimum value of $\mathrm{d}$ so that there is a dark fringe at $O.$ is given as $\sqrt{\frac{\lambda d}{\beta }}$

(b) Suppose $\mathrm{d}$ has this value then the distance $\mathrm{x}$ at which the next bright fringe is formed is given as $\alpha d$

(c) The fringe-width is given as $\gamma d$.

Find the value of $\alpha +\beta +\gamma$

The figure shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let $B{P}_0-A{P}_0=\mathrm{\lambda }/3$ and $D>>\mathrm{\lambda }$
(a) Show that in this case $d=\sqrt{2\mathrm{\lambda }D/3}.$

(b) Show that the intensity at $P_0$ is three times the intensity due to any of the three slits individually.