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Superposition and interference - class-XII

Description: superposition and interference
Number of Questions: 16
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Tags: physics wave optics optics oscillations and waves
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Two points P and Q are situated at the same distance from a source of light but on opposite sides.The phase difference between the light waves passing through P and Q will be

  1. $\pi$

  2. 2$\pi$

  3. $\pi$/2

  4. 0


Correct Option: D

Light waves of wave length $\lambda$ propagate in a medium. If $M$ and $N$ are two points on the wave front and they are separated by a distance $\lambda /4$, the phase difference between them will be (in radian)

  1. $\dfrac{\pi}{2}$

  2. $\dfrac{\pi}{8}$

  3. $\dfrac{\pi}{45}$

  4. zero


Correct Option: D

In an interference experiment, distance between the lists is $2\ mm$ and screen is placed at distance $1\ m$ from the slits. Fourth dark fringe is formed exactly opposite to one of the slits. Wavelength of light used in nm is

  1. 480

  2. 600

  3. 570

  4. 500


Correct Option: A

A glass wedge of angle $0.01$ radian and $\mu=1.5$ is illuminated by monochromatic light of wavelength $6000\ A$ falling normally on it. At what distance from wedge will $10^{th}$ dark fringe be observed by reflected light ?

  1. $0.1\ mm$

  2. $0.2\ mm$

  3. $0.3\ mm$

  4. $0.4\ mm$


Correct Option: A

In YDSE $S _1$ and $S _2$ has intersity $I$ and $9I$. Find difference in intensity b/w point which has phase difference of  $\pi$

  1. $10 I$

  2. $6 I$

  3. $8I$

  4. $4I$


Correct Option: D

For interference between waves from two sources of intensities $I$ and $4I$, find the intensity at the point in the pattern where the phase difference is $\dfrac{\pi}{2}$ and $\pi$.

  1. $10I$ and $I$

  2. $5I$ and $5I$

  3. $5I$ and $I$

  4. $5I$ and $10I$


Correct Option: C

The path difference between two interfering waves at a point on the screen  is $ \lambda /6 $. The ratio of intensity at the point and that the central bright fringe will be (Assume that internally due to each slit in same). 

  1. 0.853

  2. 8.53

  3. 0.75

  4. 7.5


Correct Option: C
Explanation:

Given that,

Path difference $x=\dfrac{\lambda }{6}$

We know that,

  $ I={{I} _{0}}{{\cos }^{2}}\left( \dfrac{\phi }{2} \right) $

 $ \dfrac{I}{{{I} _{0}}}={{\cos }^{2}}\left( \dfrac{\phi }{2} \right)....(I) $

Now, the phase difference is

  $ \phi =\dfrac{2\pi }{\lambda }\times x $

 $ \phi =\dfrac{2\pi }{\lambda }\times \dfrac{\lambda }{6} $

 $ \phi =\dfrac{\pi }{3} $

Now, put the value of $\phi $ in equation (I)

  $ \dfrac{I}{{{I} _{0}}}={{\cos }^{2}}{{30}^{0}} $

 $ \dfrac{I}{{{I} _{0}}}=\dfrac{3}{4} $

 $ \dfrac{I}{{{I} _{0}}}=0.75 $

Hence, the value of ratio of the intensity at the point is $0.75$ 

The distance between the two slits in a Young's double slit experiment is $d$ and the distance of the screen from the plane of the slits is $b$,$P$ is a point on the screen directly in front of one of the slits. The path difference between the waves arriving at $P$ from the two slits is

  1. $\dfrac{d^{2}}{b}$

  2. $\dfrac{d^{2}}{2b}$

  3. $\dfrac{2d^{2}}{b}$

  4. $\dfrac{d^{2}}{4b}$


Correct Option: B

The phase difference between two waves, represented by
${ y } _{ 1 }={ 10 }^{ -6 }sin{ 100t+(x/50)+0.5} m$
${ y } _{ 2 }={ 10 }^{ -6 }cos{ 100t+\left( \frac { x }{ 50 }  \right) } m$
where x is expressed in meters and is expressed in seconds, is approximately:

  1. 2.07 Radians

  2. 0.5 Radians

  3. 1.5 Radians

  4. 1.07 Radians


Correct Option: D

In a YDSE, the central bright fringe can be identified :

  1. as it has greater intensity than the other bright fringe.

  2. as it is wider than the other bright fringes.

  3. as it is narrower than the other bright fringes.

  4. by using white light instead of single wavelength light.


Correct Option: A

Two coherent plane light waves of equal amplitude makes a small angle $\alpha (<<1)$ with each other. They fall almost normally on a screen. If $\gamma $ is the wavelength of light waves, the fringe width $\Delta x$ of interference patterns of the two sets of wave on the screen is  

  1. $\dfrac { 2\lambda }{ \alpha } $

  2. $\dfrac { \lambda }{ \alpha } $

  3. $\dfrac { \lambda }{ (2\alpha ) } $

  4. $\dfrac { \lambda }{ \sqrt { \alpha } } $


Correct Option: B

What is the amplitude of resultant wave, when two waves $y _1=A _1\sin (\omega t-B _1)$ and $y _2=A _2\sin (\omega t-B _2)$ superimpose ?

  1. $A _1+A _2$

  2. $|A _1-A _2|$

  3. $\sqrt{A _1^2+A _2^2+2A _1A _2\cos (B _1-B _2)}$

  4. $\sqrt{A _1^2+A _2^2+2A _1A _2\cos B _1 B _2}$


Correct Option: C

An isotropic point source emits light. A screen is situated at  a given distance. If the distance between sources and screen is decreased by $2\%$, illuminance will increase by:

  1. $1\%$

  2. $2\%$

  3. $3\%$

  4. $4\%$


Correct Option: D
Explanation:
For isotropic point source
$E\propto\dfrac{1}{r^{2}}$

For small change, $\dfrac{\Delta E}{\Delta r}=\dfrac{-2k }{r^{3}}$

$\dfrac{\Delta E}{\Delta r}=-2\dfrac{k}{r^{2}}\dfrac{1}{r}$ or $\dfrac{\Delta E}{\Delta r}=-2\dfrac{E}{r}$

or $\dfrac{\Delta E}{I}=2\left(-\dfrac{\Delta r}{r}\right)\therefore \% \Delta E=2\times 2\%=4\%$

Hence, (d) is correct.

The path difference between two wavefronts emitted by coherent sources of wavelength 5460 $\overset{o}{A}$ is 2.1 micron. The phase difference between the wavefronts at that point is

  1. 7.962

  2. 7.962 $\pi$

  3. $\displaystyle\frac{7.962}{\pi}$

  4. $\displaystyle\frac{7.962}{3\pi}$


Correct Option: B
Explanation:

Phase diff. = $\displaystyle\frac{2\pi x}{\lambda}$
Path difference = $\displaystyle\frac{2\pi \times 2.1 \times 10^{-6}}{5460 \times 10^{-10}}$ = 7.692 $\pi$ radian.

Two light rays having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first ray travels a path ${L} _{1}$ through a medium of refractive index ${n} _{1}$ while the second ray travels a path of length ${L} _{2}$ through a medium of refractive index ${n} _{2}$. The two waves are then combined to produce interference. The phase difference between the two waves is:

  1. $\dfrac { 2\pi }{ \lambda } \left( { L } _{ 2 }-{ L } _{ 1 } \right) $

  2. $\dfrac { 2\pi }{ \lambda } \left( { n } _{ 1 }{ L } _{ 1 }-{ n } _{ 2 }{ L } _{ 2 } \right) $

  3. $\dfrac { 2\pi }{ \lambda } \left( { n } _{ 2 }{ L } _{ 1 }-{ n } _{ 1 }{ L } _{ 2 } \right) $

  4. $\dfrac { 2\pi }{ \lambda } \left( \dfrac { { L } _{ 1 } }{ { n } _{ 1 } } -\dfrac { { L } _{ 2 } }{ { n } _{ 2 } } \right) $


Correct Option: B
Explanation:

The optical path between any two points is proportional to the time of travel.
The distance traversed by light in a medium of refractive index $\mu $ in time $t$ is given by
$d=vt$            .....(i)


where $v$ is velocity of light in the medium. The distance traversed by light in a vacuum in this time,

$\Delta =ct$

  $=c\cdot \dfrac { d }{ v } $        [from equation (i)]

  $=d \dfrac { c }{ v } =\mu d$          .......(ii)                   (Since, $\mu =\dfrac { c }{ v } $)

This distance is the equivalent distance in vacuum and is called optical path.

Here, optical path for first ray $={ n } _{ 1 }{ L } _{ 1 }$

Optical path for second ray $={ n } _{ 2 }{ L } _{ 2 }$

Path difference $={ n } _{ 1 }{ L } _{ 1 }-{ n } _{ 2 }{ L } _{ 2 }$

Now, phase difference

    $=\dfrac { 2\pi  }{ \lambda  } \times $ path difference

    $=\dfrac { 2\pi  }{ \lambda  } \times \left( { n } _{ 1 }{ L } _{ 1 }-{ n } _{ 2 }{ L } _{ 1 } \right) $

Electrons accelerated from rest by an electrostatic potential are collimated and sent through a Young's double slit setup. The figure width is w. If the accelerating potential is doubled then the width is now close to.

  1. $0.5$ w

  2. $0.7$ w

  3. $1.0$ w

  4. $2.0$ w


Correct Option: B
Explanation:
$\beta=\dfrac{\lambda D}{d}$

$\lambda=\dfrac{h}{mV}=\dfrac{h}{\sqrt{2mq\Delta V}}$

$\beta \propto \lambda$

Therefore,

$\beta \propto \dfrac{1}{\sqrt{\Delta V}}$

$As $\Delta V$ is double,

$\beta$ is $\dfrac{1}{\sqrt 2}$ times of $\beta_{old}$

Therefore,

$\beta_{new}=0.7\beta=0.7\,w$
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