2lambda Paradox

Q. Young's double slit experiment is carried out by using green, red and blue lihgt, one color at a time. The fringe widths recorded are ${\beta }_B,{\beta }_R$ and ${\beta }_B$ respecitvley. Then,

1. ${\beta }_G>{\beta }_B>{\beta }_R$
2. ${\beta }_R>{\beta }_B>{\beta }_G$
3. ${\beta }_R>{\beta }_G>{\beta }_B$
4. ${\beta }_B>{\beta }_G>{\beta }_R$

Q. Yellow light emitted by sodium lamp in Young’s double slit experiment is replaced by monochromatic blue light of the same intensity

1. Fringe width will decrease
2. Fringe width will increase
3. Fringe width will remain unchanged
4. Fringe will become less intense

Q. If intensity of each wave in the observed interference pattern in Young's double slit experiment is $I_0$, then for some point P where the phase difference is $\varphi$, resultant intensity $I$ will be:

1. $I=I_0\cos \varphi$
2. $I=I_0{\cos }^2\varphi$
3. $I=I_0(1+\cos \varphi )$
4. $I=2I_0(1+\cos \varphi )$

Q. In Young's double slit experiment, two slits $4\text{mm}$ apart, are illuminated by a light of wavelength $600\text{nm}$. What will be the fringe width on a screen placed $2\text{m}$ from the slits?

1. $0.3\text{mm}$
2. $3\text{mm}$
3. $4\text{mm}$
4. $0.12\text{mm}$

Q. A double slit interference pattern is produced on a screen, as shown in the figure, using monochromatic light of wavelength $500nm$. Point $P$ is the location of the central bright fringe, that is produced when light waves arrive in phase without any path difference. A choice of three strips A, B and C of transparent materials with different thickness and refractive indices is available, as shown in the table. These are placed over one or both of the slits, singularly or in conjunction, causing the interference pattern to be shifted across the screen from the original pattern. In the column - I, how the strips have been placed , is mentioned whereas in the column -II, order of the fringe at point P on the screen that will be produced due to the placement of the strip (s), is shown. Correctly match both the columns.

1. $P-2,Q-2,R-4,S-1$
2. $P-3,Q-3,R-4,S-1$
3. $P-1,Q-3,R-1,S-1$
4. $P-2,Q-3,R-2,S-3$

Q. In young's double slit experiment, interference pattern is observed on the screen $L$ distance away from slits, distance between centre of two consecutive bright fringes is $x$ and slits separation is $d$, then the wavelength of light will be –

1. $\frac{xd}{L}$
2. $\frac{xL}{d}$
3. $\frac{Ld}{x}$
4. $\frac{xd}{L+x}$

Q. The double slit experiment of Young has been shown in figure. Q is the position of the first bright fringe on the right side and P is the ${11}^{th}$ bright fringe on the other side as measured from Q. If wavelength of the light used is $6000A^{\circ },$ then $S_{1}B$, will be equal to

1. $6\times {10}^{-6}m$
2. $6.6\times {10}^{-6}m$
3. $3.138\times {10}^{-7}m$
4. $3.144\times {10}^{-7}m$

Q. In Young's double slit experiment using yellow and blue lights of wavelengths $560\text{nm}$ and $420\text{nm}$ respectively, the value of $n$ for which $n^{th}$ order of yellow bright fringe coincides with $(n+1{)}^{th}$ order of blue bright fringe is

1. $3$
2. $4$
3. $2$
4. $5$

Q.

In a young's doube slit experiment using mono-chromatic light, the fringe pattern shifts by a certain distance on the screen whwen a mica sheet of refractive index 1.6 and thickness 1.964 micron $(1micron={10}^{-6}m)$ is introduced in t epath of one of th einterfering waves. The mica sheet is then removed and
the distance between the screen and the slits is doubled. It is found that the distance between teh successive maxima now is the same as the observed fringe- shift upon th eintroduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment.

Q. A beam of light consisting of two wavelength $6300A^{\circ }$ and $\lambda A^{\circ }$ is used to obtain interference fringes in a Young’s double slit experiment. If $4^{th}$ bright fringe of $6300A^{\circ }$ coincides with $5^{th}$ dark fringe of $\lambda A^{\circ }$, the value of $\lambda \left(\text{in}{A}^{\circ }\right)$ is

1. $5200$
2. $4800$
3. $6200$
4. $5600$

Q. In a Young's double slit experiment two slits are separated by $2\text{mm}$ and the screen is placed one meter away. When a light of wavelength $500\text{nm}$ is used, the fringe separation will be:

1. $0.75\text{mm}$
2. $0.50\text{mm}$
3. $1\text{mm}$
4. $0.25\text{mm}$

Q. A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart

Find out the minimum order of the bright fringe that would not be visible

Q. In Young's double slit interference experiment the wavelength of light used is 6000A. If the path difference between waves reaching a ponit P on the screen is 1.5 microns, then at that point P:

1. second bright band occurs
2. second dark band occurs
3. third dark band occurs
4. thirdbright band occurs

Q.

What is the error in the reasoning?

1. The slit is too big.

2. The resultant of waves from each pair of points are not in the same phase, so they will not interfere constructively.

3. Interference will not happen.
4. Intensity is not given.

Q.

Plane microwaves are incidnet on a long slit having a width of 5.0 cm. Calculate the wavelength of the microwaves if the first diffraction m8inimum is formed at $\theta ={30}^{\circ }$

Q. Interference fringes are produced by a double slit arrangement and a piece of plane parallel glass slab $(\mu =1.5)$ is placed in front of one of the slits. If the fringes are displaced through a distance equal to $30$ fringe widths for light of wavelength $6000\mathring{\text{A}}$, find the thickness of the glass slab.

1. $0.36\mu \text{m}$
2. $360\mu \text{m}$
3. $3.6\mu \text{m}$
4. $36\mu \text{m}$

Q. In young's double slit experiment the fringe width with light of wave length 6000 A is found to be 4.0mm. What will be the fringe width if light of wavelength 4800 A is used?

1. 2.8mm
2. 3.2mm
3. 4.0mm
4. 4.8mm

Q.

What is the error in the reasoning?

1. It's right, this is a tragedy, the world is gonna get destroyed.

2. The resultant of waves from each pair of points are not in the same phase, so they will not interfere constructively.

3. \N
4. \N

Q. A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart. If the light wavelength is changed to $450\text{nm}$, then what can be commented regarding the width of the central maxima and the number of bright interference fringes it encloses?

1. Increases
2. Decreases
3. Remains Same
4. Becomes zero

Q. The position of the direct image obtained at O${}_3$, when a monochromatic beam of light is passed through a plane transmission grating at normal incidence as shown in Fig. The diffracted images A, B and c correspond to the first, second and third order diffraction. when the source is replaced by another source of shorter wave-length

1. all the four will shift in the direction O to C
2. the images C, B and A will shift away from O
3. all the four will shift in the direction C to O
4. the images C, B and A will shift towards O

Q. In Young's double slit interference experiment, the wavelength of light used is $6000\dot{A}$. If the path difference between waves reaching a point P on the screen is 1.5 microns, then at that point P

1. Second maxima occurs
2. Second minima occurs
3. Third minima occurs
4. Third maxima occurs

Q. A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart. If the light wavelength is changed to $450\text{nm}$, then what can be commented regarding the width of the central maxima and the number of bright interference fringes it encloses?

1. Increases
2. Decreases
3. Remains Same
4. Becomes zero

Q. A sky wave with a frequency $55$ MHz is incident on $D$-region of earth's atmosphere at ${45}^{\circ }$. The angle of refraction is (electron density for $D$ region is $400$ electron/ 3 ${cm}^3$

1. ${60}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$
4. ${15}^{\circ }$

Q. The condition for diffraction of $mth$ order minima is

1. $d\sin {\theta }_m=m\lambda ,m=1,2,3,....$
2. $d\sin {\theta }_m=\frac{m\lambda ,}{2}m=1,2,3,....$
3. $d\sin {\theta }_m=(m+1)\frac{\lambda }{2},m=1,2,3,....$
4. $d\sin {\theta }_m=(m-1)\frac{\lambda }{2},m=1,2,3,....$

Q. A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart. If the light wavelength is changed to $450\text{nm}$, then what can be commented regarding the width of the central maxima and the number of bright interference fringes it encloses?

1. Increases
2. Decreases
3. Remains Same
4. Becomes zero

Q. If two identical waves interfere at a point in the same medium, then the resultant wave has the same _________ as of the interfering waves.

1. angular frequency
2. wave number
3. Both options $\left(A\right)$ and $\left(B\right)$
4. None of these

Q. A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart

Find out the minimum order of the bright fringe that would not be visible

Q. A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart

Find out the minimum order of the bright fringe that would not be visible