Two transparent slabs having equal thickness but different refractive indices ${\mathrm{\mu }}_1$ and ${\mathrm{\mu }}_2$ are pasted side by side to form a composite slab. This slab is placed just after the double slit in a Young's experiment so that the light from one slit goes through one material and the light from the other slit goes through the other material. The minimum thickness of the slab so that there is a minimum at the point ${\mathrm{P}}_0$ which is equidistant from the slits is $\frac{\lambda }{x\left|{\mu }_1-{\mu }_2\right|}$. Find $x$.

A thin paper of thickness $0.02 \mathrm{mm}$ having a refractive index $1.45$ is placed across one of the slits in Young's double-slit experiment. The paper transmits $\frac{4}{9}\mathrm{th}$ of the light energy falling on it.

(a) Find the ratio of the maximum intensity to the minimum intensity in the fringe pattern.

(b) How many fringes will cross through the centre if an identical paper piece is placed on the other slit also? The wavelength of the light used is $600 \mathrm{nm}$.

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?