Tag: coherence

Questions Related to coherence

To demonstrate the phenomenon of interference we require two sources which emit radiation of

physics superposition of waves coherence young's double slit experiment interference

  1. nearly the same frequency

  2. the same frequency

  3. different wavelength

  4. the same frequency and having a definite phase relationship

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Correct Option: D

Which of the following is not an essential condition for interference?

physics superposition of waves coherence young's double slit experiment interference

  1. The two interfering waves must propagate in almost the same direction

  2. The waves must have the same period and wavelength

  3. The amplitudes of the two waves must be equal

  4. The two interfering beams of light must originate from the same source

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Correct Option: A
Explanation:

When two waves are propagate in same direction

If two sources have a randomly varying phase difference $\varphi ( t )$  the resultant intensity will be given by 

physics superposition of waves coherence young's double slit experiment interference

  1. $I _ { 0 }$

  2. $\dfrac { I _ { 0 } } { 2 }$

  3. $2 I _ { 0 }$

  4. $\dfrac { I _ { 0 } } { \sqrt { 2 } }$

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Correct Option: C
Explanation:

Phase difference is $\phi (t)$,

Since, the phase difference is varying, then the waves are said to be incoherent. So, the intensity of resultant wave is the sum of intensities of each wave i.e. $2\,{{I} _{0}}$ 

In a biprism experiment, the distance of 20 th bright bandfrom the center of the interference pattern is 8$\mathrm { mm }$ . The distance of 30th bright band from the center is

physics superposition of waves coherence young's double slit experiment interference

  1. $11.8\mathrm { mm }$

  2. 12$\mathrm { mm }$

  3. 14$\mathrm { mm }$

  4. 16$\mathrm { mm }$

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Correct Option: A
Explanation:

Given

$\begin{array}{l} 20\beta =8mm \ \beta =\dfrac { 8 }{ { 20 } }  \ Now, \ 30th\, \, \max  ima=30\beta =\dfrac { { 30\times \beta  } }{ { 20 } } =12mm \ 30th\, \min  ima=\dfrac { { \left( { 2\left( { 30 } \right) -1 } \right)  } }{ 2 } \beta  \ =\dfrac { { 59 } }{ 2 } \beta  \ =\dfrac { { 59 } }{ 2 } \times \dfrac { 8 }{ { 20 } }  \ =11.8mm \ Hence,\, option\, A\, is\, the\, correct\, answer. \end{array}$

Two coherent waves of light will not produce constructive interference if the phase difference between them is

physics superposition of waves coherence young's double slit experiment interference

  1. $0^0$

  2. $360^0$

  3. $720^0$

  4. $90^0$

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Correct Option: D
Explanation:

Constructive interference for coherent waves takes place when phase difference = $2n\pi$ where n is a integer

So the only case in the options when constructive interference will not take place is $90^\circ$

Answer. D

The time of coherence is of the order of

physics superposition of waves coherence young's double slit experiment interference

  1. $10^{-4}s$

  2. $10^{-8}s$

  3. $10^{-6}s$

  4. $10^{-2}s$

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Correct Option: B
Explanation:

In a light source, a light wave(photon) is produced when an excited atom goes to the ground state and emits light.

The duration of this transition is $10^{-8}s$. Thus the emitted wave remains sinusoidal for this much time. This time is known as coherence time($\tau _c$).

The time of coherence is of the order of 

physics superposition of waves coherence young's double slit experiment interference

  1. $10^{-4}s$

  2. $10^{-8}s$

  3. $10^{-6}s$

  4. $10^{-2}s$

Show answer
Correct Option: B
Explanation:

In a light source(photon) is produced when an excited atom goes to the ground state and emits light.

The duration of the transition is about $10^{-8}s$. Thus the emitted light remains sinusoidal for this much time. This is called the coherence time($\tau _c$).

Which of the following, cannot produce two coherent sources?

physics superposition of waves coherence young's double slit experiment interference

  1. Lloyd's mirror

  2. Fresnel biprism

  3. Young's double sit

  4. Prism

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Correct Option: D
Explanation:

Two coherent sources are produced in Lloyd's mirror by reflection of light from a plane mirror, hence the original source and its image acting as coherent sources.

In fresnel biprism, light from a point source gets refracted by a biprism to produce two coherent sources.
In Young's double slit, two coherent sources are produced by passing of light from a single source through two slits.

The device which produces highly coherent sources  is

physics superposition of waves coherence young's double slit experiment interference

  1. Fresnel biprism

  2. Young's double sit

  3. Laser

  4. Lloyd's mirror

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Correct Option: C
Explanation:

The atoms in the laser medium are pumped up energetically by an external power source, producing a population inversion of atomic energies. The pumped-up atoms can return to lower energy levels by emitting light at only certain frequencies, depending on the particular medium, which can be a solid (e.g. laser diode), a liquid (e.g. dye laser) or a gas (e.g. helium-neon laser).

We get temporal coherence because the excited atoms emit only at that preferred frequency.

Two sources are called coherent if they produce waves

physics superposition of waves coherence young's double slit experiment interference

  1. of equal wavelength

  2. of equal velocity

  3. having same shape of wavefront

  4. having a constant phase different

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Correct Option: D
Explanation:

Two source are called coherent, if they have constant phase difference i.e., phase difference between two wave is constant with respect to time.