Answer the Following Question. Describe Any Two Characteristic Features Which Distinguish Between Interference and Diffraction Phenomena. Derive the Expression for the Intensity - Physics

Answer in Brief

Answer the following question.
Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double-slit experiment.



Difference between interference and diffraction:
In the interference pattern, the intensity of the dark fringe is completely zero.
In the diffraction pattern, the intensity of secondary minima is minimum, but not completely zero.
In interference pattern the width of all the interference fringes is equal. In diffraction pattern the width of central maxima is large, and on increasing distance, the width of maxima decreases.
In interference pattern the intensity of all the bright bands is equal.
In the diffraction pattern, the intensity of all the secondary maxima is not equal.  

The principle of superposition of light waves:
When two or more wave trains of light travelling in a medium superpose upon each other, the resultant displacement at any instant is equal to the vector sum of the displacements due to individual waves.

If `vecy_1,vecy_2,vecy_3,....` be the displacements due to different waves, then the resultant displacement is given by, `vecy = vecy_1 + vecy_2 + vecy_3 +` ... conditions for constructive and destructive interference:

Let  the displacement of the waves from the source `S_1` and `S_2` at a point P on the screen at any time 't' be given by,
`"y"_1 = a_1 sin omegat`
`"y"_2 = a_2 sin(omegat + phi)`
where `phi` is the constant phase difference between the two waves
by the superposition principal , the resultant displacement at point P is given by,

`"y" = "y"_1 + "y"_2`

= `a_1 sin omegat + a_2 sin (omegat + phi)`

= `a_1 sin omegat + a_2 sin omegat cos phi + a_2 cos omegat sin phi`

`y = (a_1 + a_2 cos phi) sin omegat + a_2 sin phi cos omegat`  ...(i)

Let `a_1 + a_2 cos phi = A cos theta` ...(ii)

`a_2 sin phi = A sin theta`  ...(iii)

Then, equation (i) becomes
`"y" = Acostheta sin omegat + A sin theta cos omegat`

`"y" = Asin(omegat + theta)`

Squaring and adding both sides of the equations (ii) and (iii), we obtain

`A^2 cos^2theta + A^2 sin^2 theta = (a_1 + a_2 cos phi)^2 + a_2^2 sin^2 phi`

`A^2 = a_1^2 + a_2^2 (cos^2phi + sin^2phi) + 2a_1a_2 cos phi`

`A^2 = a_1^2 + a_2^2 + 2a_1a_2 cos phi`

The intensity of light is directly proportional to the square of the amplitude of the wave. The intensity of light at point P on the screen is given by,

`I = a_1^2 + a_2^2 + 2a_1a_2 cos phi`     ...(iv)

Concept: Interference
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2018-2019 (March) 55/1/3

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Write the important characteristic features by which the interference can be distinguished from the observed diffraction pattern.

Write the necessary conditions to obtain sustained interference fringes.

State any one difference between interference of light and diffraction of light

Laser light of wavelength 630 nm is incident on a pair of slits which are separated by 1.8 mm. If the screen is kept 80 cm away from the two slits, calculate:

1) fringe separation i.e. fringe width.

2) distance of 10th bright fringe from the centre of the interference pattern

When a drop of oil is spread on a water surface, it displays beautiful colours in daylight because of ______________ .

Four light waves are represented by

(i) \[y =  a_1   \sin  \omega t\]

(ii) \[y =  a_2   \sin  \left( \omega t + \epsilon \right)\]

(iii) \[y =  a_1   \sin  2\omega t\]

(iv) \[y =  a_2   \sin  2\left( \omega t + \epsilon \right).\]

Interference fringes may be observed due to superposition of

(a) (i) and (ii)

(b) (i) and (iii)

(c) (ii) and (iv)

(d) (iii) and (iv)

A narrow slit S transmitting light of wavelength λ is placed a distance d above a large plane mirror, as shown in the following figure. The light coming directly from the slit and that coming after the reflection interfere at a screen ∑ 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?

A long narrow horizontal slit is paced 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1.0 m away from the slit. Find the fringe-width if the light used has a wavelength of 700 nm.

A long narrow horizontal slit is paced 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1.0 m away from the slit. If the mirror reflects only 64% of the light energy falling on it, what will be the ratio of the maximum to the minimum intensity in the interference pattern observed on the screen?

The intensity at the central maximum (O) in a Young’s double slit experimental set-up shown in the figure is IO. If the distance OP equals one-third of the fringe width of the pattern, show that the intensity at point P, would equal `(I_0)/4`.

In Young’s double slit experiment, the slits are separated by 0.5 mm and screen is placed 1.0 m away  from the slit. It is found that the 5th bright fringe is at a distance of 4.13 mm from the 2nd dark fringe.  Find the wavelength of light used.  

Why are multiple colours observed over a thin film of oil floating on water? Explain with the help of a diagram.

Answer in brief:

Explain what is the optical path length. How is it different from actual path length?

Answer in brief:

What is meant by coherent sources?

Answer in brief:

In Young's double-slit experiment what will we observe on the screen when white light is incident on the slits but one slit is covered with a red filter and the other with a violet filter? Give reasons for your answer.

Describe Young's double-slit interference experiment and derive conditions for occurrence of dark and bright fringes on the screen. Define fringe width and derive a formula for it.

What are the conditions for obtaining a good interference pattern? Give reasons.

What are the two methods for obtaining coherent sources in the laboratory?

A double-slit arrangement produces interference fringes for sodium light (λ = 589 nm) that are 0.20° apart. What is the angular fringe separation if the entire arrangement is immersed in water (n = 1.33)?

The intensity of the light coming from one of the slits in Young's experiment is twice the intensity of the light coming from the other slit. What will be the approximate ratio of the intensities of the bright and dark fringes in the resulting interference pattern?

Why two light sources must be of equal intensity to obtain a well-defined interference pattern?

Draw a neat labelled ray diagram of the Fresnel Biprism experiment showing the region of interference. 

What is interference?

Describe geometry of the Young’s double slit experiment with the help of a ray diagram. What is fringe width? Obtain an expression of it. Write the conditions for constructive as well as destructive interference. 

Explain constructive and destructive interference with the help of a diagram?

In a Young’s double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to ______.

One of Young’s double slits is covered with a glass plate as shown in figure. The position of central maximum will,

What is phase of a wave?

What is intensity (or) amplitude division?

How does wavefront division provide coherent sources?

How do source and images behave as coherent sources?

What is a bandwidth of interference pattern?

Obtain the equation for resultant intensity due to interference of light.

Explain Young’s double-slit experimental setup and obtain the equation for path difference.

Discuss the interference in thin films and obtain the equations for constructive and destructive interference for transmitted and reflected light.

Does diffraction take place at Young’s double-slit?

In Young’s double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength λ0 = 750 nm and λ = 900 nm. What is the minimum distance from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other?

In Young’s double-slit experiment, 62 fringes are seen in the visible region for sodium light of wavelength 5893 Å. If violet light of wavelength 4359 Å is used in place of sodium light, then what is the number of fringes seen?

The ratio of maximum and minimum intensities in an interference pattern is 36 : 1. What is the ratio of the amplitudes of the two interfering waves?

Light of wavelength 600 nm that falls on a pair of slits producing interference pattern on a screen in which the bright fringes are separated by 7.2 mm. What must be the wavelength of another light which produces bright fringes separated by 8.1 mm with the same apparatus?

In Young's double-slit experiment, if the width of the 2nd bright fringe is 4 x 10-2 cm, then the width of the 4th bright fringe will be ______ cm.

If the monochromatic source in Young's double slit experiment is white light, then ____________.

The phenomenon of interference is based on ______.

In a biprism experiment, red light of wavelength 6500 Å was used. It was then replaced by green light of wavelength 5200 Å. The value of n for which (n + 1)th green bright band would coincide with nth red bright band for the same setting is ______.

Two identical light sources s1 and s2 emit light of same wavelength `lambda`. These light rays will exhibit interference if their ______.

In biprism experiment, if the 5th bright band with wavelength 'λ1' coincides with the 6th dark band with wavelength 'λ2' then the ratio `(lambda_2/lambda_1)` is ______ 

The graph shows the variation of fringe width (β) versus distance of the screen from the plane of the slits (D) in Young's double-slit experiment Keeping other parameters the same. The wavelength of light used can be calculated as d = distance between the slits ______ 


In Young's double-slit experiment, if the two sources of light are very wide, then ______.

Two coherent sources of intensities I1 and I2 produce an interference pattern on the screen. The maximum intensity in the interference pattern is ______

If we have two coherent sources S1 and S2 vibrating in phase, then for an arbitrary point P constructive interference is observed whenever the path difference is ______.

What is meant by Constructive interference?

A beam of electrons is used in Young's double-slit experiment. If the speed of electrons is increased then the fringe width will ______.

How will the interference pattern of Young's double slit change if one of the two slits is covered by a paper which transmits only half of the light intensity?

Show graphically the intensity distribution in a single slit diffraction pattern.

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is ______ nm.

Two coherent sources P and Q produce interference at point A on the screen where there is a dark band which is formed between 4th bright band and 5th bright band. Wavelength of light used is 6000 Å. The path difference between PA and QA is ______.

In a double-slit experiment, the optical path difference between the waves coming from two coherent sources at a point P on one side of the central bright is 7.5 µm and that at a point Q on the other side of the central bright fringe and 1.8 µm. How many bright and dark fringes are observed between points P and Q if the wavelength of light used is 600 nm?

Describe Young's double-slit interference experiment.

With a neat labelled ray diagram explain the use of Fresnel's biprism to obtain two coherent sources.

In biprism experiment, the distance of 20th bright band from the central bright band is 1.2 cm. Without changing the experimental set-up, the distance of 30 bright band from the central bright band will be ______.


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