Young's Double Hole Experiment

Q. In a Young's double slit experiment, the distance between the $3^{\text{rd}}$ bright fringe and $6^{\text{th}}$ dark fringe both lying on the same side of the central maximum is $3\text{mm}$. What is the distance of $2^{\text{nd}}$ dark fringe from the central maximum?

1. $0.6\text{mm}$
2. $1.2\text{mm}$
3. $1.8\text{mm}$
4. $2.4\text{mm}$

Q. In a Young's double slit experiment, the ratio of the slit's width is $4:1$. The ratio of the intensity of maxima to minima, close to the central fringe on the screen will be

1. $9:1$
2. $(\sqrt{3}+1{)}^4:16$
3. $25:9$
4. $4:1$

Q. Consider a Young's double slit experiment as shown in figure. What should be the slit separation $d$ in terms of wavelength $\lambda$ such that the first minima occurs directly in front of the slit $S_1$ ?

1. $\frac{\lambda }{(5-\sqrt{2})}$
2. $\frac{\lambda }{(\sqrt{2}-2)}$
3. $\frac{\lambda }{2(5-\sqrt{2})}$
4. $\frac{\lambda }{2(\sqrt{5}-2)}$

Q.

How does the spacing of bright fringes in the two slit arrangement change when we increase the spacing between the slits?

Q. At two points $P$ and $Q$ on a screen in Young's double slit experiment, waves from slits $S_1$ and $S_2$ have a path difference of $0$ and $\frac{\lambda }{4}$ respectively. The ratio of intensities at $P$ and $Q$ will be:

1. $2:1$
2. $\sqrt{2}:1$
3. $4:1$
4. $3:2$

Q. In Young's double slit experiment, the fringe pattern is observed on a screen placed at a distance $D$. The slits are illuminated by light of wavelength $\lambda$. The distance from the central point where the intensity falls to half the maximum is

1. $\frac{\lambda D}{4d}$
2. $\frac{\lambda D}{d}$
3. $\frac{\lambda D}{2d}$
4. $\frac{\lambda D}{3d}$

Q. In a YDSE arrangement separation between slits is d, screen is at distance D from the slits, and $\lambda$ is wavelength of light used.If intensity of light from each slit on the screen is $I_0$, then the minimum seperation between two lines on the screen, where intensity is $I_0$, is

1. $\frac{2\lambda D}{3d}$
2. $\frac{\lambda D}{3d}$
3. $\frac{3\lambda D}{4d}$
4. $\frac{\lambda D}{2d}$

Q. The principal section of glass prism is an isosceles ΔPQR with PQ = PR. The face PR is silvered. A ray is incident perpendicularly on face PQ, and after two reflections, it emerges from base QR, normal to it. Find the angle (in degree) of the prism.

Q. In a Young's double slit experiment, $16$ fringes are observed in a certain segment of the screen when light of wavelength $700\text{nm}$ is used. If the wavelength of light is changed to $400\text{nm}$, the number of fringes observed in the same segment of the screen would be

1. $24$
2. $30$
3. $18$
4. $28$

Q. A right-angled prism is to be made by selecting a proper material and the angles $A$ and $B$ $(B\le A)$, as shown in the figure. It is desired that a ray of light incident on the face $AB$ emerges parallel to the incident direction after two internal reflections. What should be the minimum refractive index above which the internal reflections happens?

1. $\sqrt{2}$
2. $\sqrt{3}$
3. $\sqrt{5}$
4. $\sqrt{6}$

Q. Consider a usual set-up Young's double slit experiment with slits of equal intensity as shown in the figure. Take $O$ as origin and the $y$-axis as indicated. If average intensity of light at all points between $y_1=-\frac{\lambda D}{4d}$ and $y_2=+\frac{\lambda D}{4d}$ equals $n$ times the intensity of central maxima, then $n$ equals (take average over phase difference)

1. $\frac{1}{2}(1+\frac{2}{\pi })$
2. $2(1+\frac{2}{\pi })$
3. $\frac{1}{2}(1-\frac{2}{\pi })$
4. $(1+\frac{2}{\pi })$

Q. A double-slit arrangement produces interference fringes for sodium light of, wavelength $589\text{nm}$. For what wavelength, would the fringe width, be $10$% greater?

1. $527\text{nm}$
2. $648\text{nm}$
3. $722\text{nm}$
4. $449\text{nm}$

Q. In the arrangement shown in the figure, slits $S_3$ and $S_4$ are having a variable separation $Z$. Point $O$ on the screen is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4$.
When $Z=\frac{\lambda D}{2d}$ the intensity measured at $O$ is $I_0$. The intensity at $O$ when $Z=\frac{2\lambda D}{d}$ is

1. $I_0$
2. $2I_0$
3. $3I_0$
4. $4I_0$

Q. A Lloyd’s mirror of length 5 cm is illuminated with monochromatic light of wavelength $\lambda (=6000\stackrel{\circ }{A})$ from a narrow 1 mm slit in its plane and $5\text{cm}$ plane from its near edge. Find the fringe width on a screen $120\text{cm}$ from the slit and width of interference pattern on the screen.

1. $0.036cm,1.2cm$
2. $1.2cm,0.036cm$
3. $3.6cm,0.12cm$
4. $0.045cm,0.96cm$

Q. In the arrangement shown in figure, slits $S_1$ and $S_4$ are having a variable separation Z. Point O on the screen is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4$.


The minimum value of $Z$ for which the intensity at $O$ is zero is

1. $\frac{\lambda D}{2d}$
2. $\frac{2\lambda D}{d}$
3. $\frac{\lambda D}{3d}$
4. $\frac{\lambda D}{d}$

Q.

A narrow slit S transmitting light of wavelength $\lambda$ is placed a distance d above a large plane mirror as shown in figure (17-E1). The light coming directly from the slit

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

Q. Two small angled transparent prisms (each of refracting angle $A=1^{\circ }$) are so placed that their bases coincide, so that common base is BC. This device is called Fresnel’s biprism and is used to obtain coherent sources of a point source S illuminated by monochromatic light of wavelength $6000\stackrel{\circ }{A}$ placed at a distance $a=20\text{cm}$. Calculate the separation between coherent sources. If a screen is placed at a distance $b=80$\text{cm}\) from the device, what is the fringe width of fringes (in cm) obtained
(Refractive index of material of each prism = 1.5).

Q.

At what angle in degrees should a ray of light be incident on the face of a prism of refracting angle ${60}^o$ so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is $1.524$. Given $si{n}^{-1}\left(0.66\right)={41}^o$, $\sin {19}^o=0.3256$, ${\sin }^{-1}\left(0.4962\right)={30}^o$, $\frac{1}{1.5424}=0.66$

Q. When white light passes through a thin glass prism, one gets spectrum on the other side of the prism. In the emergent beam, the ray which is deviating least is :

1. Violet ray
2. Green ray
3. Red ray
4. Yellow ray

Q. In a Young's double slit experiment, the intensity at the central maximum is $I_0$. The intensity at a distance $\beta /4$ from the central maximum is ($\beta$ is fringe width )

1. $I_0$
2. $\frac{I_0}{2}$
3. $\frac{I_0}{\sqrt{2}}$
4. $\frac{I_0}{4}$

Q. In Young's double slit experiment, the distance of the $n^{th}$ dark fringe from the centre is-

1. $(2n-1)\left(\frac{\lambda D}{2d}\right)$
2. $n\left(\frac{\lambda D}{2D}\right)$
3. $(2n-1)\left(\frac{4d}{\lambda D}\right)$
4. $n\left(\frac{2d}{\lambda D}\right)$

Q.

In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid-point of screen with ${}^{\prime }{\mu }^{\prime }$ will be best represented by $\mu \ge 1$. [Assume slits of equal width and there is no absorption by slab]

1. 

2. 

3. 

4. 

Q. In Young's double slit experiment, having slits of equal width, $\beta$ is the fringe width and $I_0$ is the maximum intensity. At a distance $x$ from the central bright fringe, the intensity will be,

1. $I_0\cos \left(\frac{x}{\beta }\right)$
2. $I_0{\cos }^2\left(\frac{2\pi x}{\beta }\right)$
3. $I_0{\cos }^2\left(\frac{\pi x}{\beta }\right)$
4. $\frac{I_0}{4}{\cos }^2\left(\frac{\pi x}{\beta }\right)$

Q. Where should we place a film of refractive $\mu =1.5$ and what should be its thickness so that maxima of zero order is obtained at O.

1. Infront of $S_1,20\mu m$
2. Infront of $S_2,20\mu m$
3. Infront of $S_1,10\mu m$
4. Infront of $S_2,10\mu m$

Q. If one of the slits of a standard Youngs double-slit experiment is covered by a thin parallel sides glass slab so that it transmits only one-half the light intensity of the other, then

1. The fringe pattern will get shifted away from the covered slit
2. The fringe width will remain unchanged
3. The fringe pattern will get shifted towards the covered slit
4. The bright fringes will become less bright and the dark ones become more bright

Q. Let the x-z plane be the boundary between transparent media. Medium 1 m in $Z\ge 0$ refractive index of $\sqrt{2}$ and medium 2 with has a refractive index of $\sqrt{3}$.
A ray of light in medium 1 given by the $\overline{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the separation. The angle of refraction in meter is :

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${75}^{\circ }$

Q. A monochromatic beam of light falls on YDSE apparatus at some angle (say $\theta$ ) as shown in the figure. A thin sheet of glass is inserted in front of the lower slit $S_2.$ The central bright fringe (path difference $=0$) will be obtained is-

1. $\text{At O}$
2. $\text{Above O}$
3. $\text{Below O}$
4. $\text{Anywhere depending on angle}\theta ,\text{thickness of plate}t,\text{and refractive index of glass}\mu$

Q. In the arrangement shown in the figure, slits $S_3$ and $S_4$ are having a variable separation $Z$. Point $O$ on the screen is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4$.
When $Z=\frac{\lambda D}{2d}$ the intensity measured at $O$ is $I_0$. The intensity at $O$ when $Z=\frac{2\lambda D}{d}$ is $n{I}_0$. Find the value of $n$.

Q. The number of waves in a glass slab of thickness $4$ cm is the same as in a water column of height $5$ cm, when the same monochromatic ray of light travels through them. What is the refractive index of water if the refractive index of glass is $\frac{5}{3}$?

1. $1.25$
2. $1.5$
3. $1.33$
4. $1.75$

Q. Consider a plane inclined at an angle ${45}^{\circ }$ with the horizontal has two slits ($S_{1}and{S}_2$ separated by a distance d = $\sqrt{2}$ mm The screen is placed at a distance of D = 10 m A parallel monochromatic light beam of wavelength 5000 $\stackrel{\circ }{A}$ is incident on the slits as shown If the fringe width of interference pattern on the screen is $k\times {10}^{-3}$ meter then find the value of k