Maxima & Minima in YDSE

Q. Young's double-slit experiment is carried with two thin sheets of thickness $10.4\mu m$ each and refractive index ${\mu }_1=1.52$ and ${\mu }_2=1.40$ covering the slits $S_1$ and $S_2$ respectively. If white light of range $400\text{nm}$ to $780\text{nm}$ is used, then which wavelength will form maxima at point $O$, the center of the screen?

1. $416\text{nm}$ only
2. $624\text{nm}$ only
3. $416\text{nm}$ and $624\text{nm}$ only
4. None of these

Q.

In Young's double slit experiment, white light is used. The separation between the slits is b. The screen is at a distance d (d>> b) from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

[IIT 1984; AIIMS 1995]

1. $\lambda =\frac{b^2}{d}$

2. $\lambda =\frac{2b^2}{d}$

3. $\lambda =\frac{b^2}{3d}$

4. $\lambda =\frac{2b^2}{3d}$

Q. Two slits separated by a distance of $1mm$ are illuminated with red light of wavelength $6.5\times {10}^{-7}m$. The interference fringes are observed on a screen placed $1m$ from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to

1. $0.65mm$
2. $1.625mm$
3. $3.25mm$
4. $0.975mm$

Q. Consider two coherent monochromatic sources $S_1$ and $S_2$, each of wavelength $\lambda$ and separated by a distance $d$. The ratio of the intensity of $S_1$ and $S_2$ is $4$. A detector moves on the line perpendicular to $S_1{S}_2$ as shown in the figure. If the resultant intensity at point $P$ is equal to $\frac{9}{4}$ times intensity of $S_1$, then the distance of $P$ from $S_1$ is,
(Given : $d>0$ and $n$ is a positive integer)

1. $\frac{d^2-n^2{\lambda }^2}{2n\lambda }$
   
2. $\frac{d^2+n^2{\lambda }^2}{2n\lambda }$
   
3. $\frac{n\lambda d}{\sqrt{d^2-n^2{\lambda }^2}}$
   
4. $\frac{2n\lambda d}{\sqrt{d^2-n^2{\lambda }^2}}$
   

Q. In YDSE apparatus shown in figure wavelength of light used is $\lambda$. The screen is moved away from the source with a constant speed $v$. Initial distance between screen and plane of slits was $D$ and at point $P$ on screen, $n^{th}$ order bright fringe is observed.

As the screen moves away value of $n$ will

1. increase
2. decrease
3. remain constant
4. first increase then decrease

Q. Consider the arrangement shown in the figure (17-E7). By some mechanism, the separation between the slits S₃ and S₄ can be changed. The intensity is measured at the point P, which is at the common perpendicular bisector of S₁S₂ and S₂S₄. When $z=\frac{D\lambda }{2d}$, the intensity measured at P is I. Find the intensity when z is equal to

$\left(\mathrm{a}\right)\frac{D\lambda }{d},\left(\mathrm{b}\right)\frac{3D\lambda }{2d}\mathrm{and}\left(\mathrm{c}\right)\frac{2D\lambda }{d}.$

Figure

Q. In a Young's double slit experiment for interference of light, the slits are $0.2\text{cm}$ apart and are illuminated by yellow light$(\lambda =600\text{nm})$. What would be the fringe width on a screen placed $1\text{m}$ from the plane of slits if the whole system is immersed in water of refractive index $\frac{4}{3}.$

1. $0.225\text{mm}$
2. $2.25\text{mm}$
3. $0.125\text{mm}$
4. $1.25\text{mm}$