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Interference Of Light - Condition And Types MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Interference of light waves- 1, Interference of light waves- 2 is considered one of the most asked concept.

  • 30 Questions around this concept.

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Two waves \mathrm{y}_{1}=\mathrm{A}_{1} \sin \left(\omega \mathrm{t}-\beta_{1}\right) and \mathrm{y}_{2}=\mathrm{A}_{2} \sin \left(\omega \mathrm{t}-\beta_{2}\right) superimpose to form a resultant wave. The amplitude of this resultant wave is given by

The time of exposure for a photographic print is 10 seconds when a lamp of 50 cd is placed at 1 m from it. Then another lamp of luminous intensity I is used and is kept at 2 m from it. If the time of exposure now is 20 s, the value of I (in cd) is

A parallel beam of white light falls on a thin film whose refractive index is 1.33. If the angle of incidence is 52^{\circ}, then the thickness of the film for the reflected light to be coloured yellow (\lambda=6000 \AA) most intensively must be

In the following passage there are blanks, each of which has been numbered and one word has been suggested alongside the blank. These numbers are printed below the passage and against each, five options are given. Find out the appropriate word which fits the blank appropriately. If the word written alongside the blank fits the passage, choose option ‘e’ (No correction required) as the correct choice.

India's semi-high-speed train Vande Bharat Express which was rallied (91)_______off by PM Narendra Modi, breaks down around 5.30 am this morning on its return from Varanasi to Delhi.According to railway officials who didn't want to be confused (92)__________, there was a major technical fault that led to break locking and wheel friction. To add on there was partial (93)_______ power failure to four coaches. Till 7.50 am the Indian Railways failed to identify and worsen (94)______ the problem. On the question of whether the Train 18 or Vande Bharat Express was fit for commercial run, railway officials were loquacious (95)_______. Notably, Train 18 is completely booked and has waiting list till February 24. Vande Bharat Express is expected (96)_________ to start its commercial operations.The reporter who was on board along with few other media officials felt suddenbreaks (97)__________ being applied around 5.30 am at Barhan around 18 km from Tundla station. A railway official on condition of anonymity said, "If the engineers are unable to rectify the problem, the train would be pushed (98)________ using another engine. But there would be problem in loosening the (99)______ engine. The engine coupler is covered, and the coupler cover needs to be removed.The train expanded (100)________ its operations around 10.30 am and reached New Delhi railway station at 1pm. According to railway officials the train was driven at speed of around 100km/h on enroute to Delhi after rectifying the fault.

What should come in the place of 94?

Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S1)?

 

The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio \frac{{I_{\max } - I_{\min } }} {{I_{\max } + I_{\min } }} will be :

In the Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is \lambda is K, (\lambda being the wave length of light used). The intensity at a point where the path difference is \frac{\lambda }{4}, will be:

In Young's double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double of that from the other slit. If I be the maximum intensity, the resultant intensity I when they  interfere at phase difference  \phiis given by :

A ray of light of intensity I is incident on a parallel glass slab at point A as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, 25% of incident energy is reflected. The rays AB and AB undergo interference. The ratio of Imax and Imin is :

 

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The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio ImaxIminImax+Imin will be

Concepts Covered - 2

Interference of light waves- 1

In order to observe interference in light waves, the following conditions must be met:

  •  The sources must be coherent.
  • The source should be monochromatic (that is, of a single wavelength).

Coherent sources-

Two sources are said to be coherent if they produce waves of the same frequency with a constant phase difference.  

  • - The relation between Phase difference (Δϕ) and Path difference (Δx)

    Phase difference (Δϕ)
    The difference between the phases of two waves at a point is called phase difference.
    i.e. if y1=a1sinωt and y2=a2sin(ωt+ϕ) so phase difference =ϕ

    Path difference (Δx) :
    The difference in path lengths of two waves meeting at a point is called path difference between the waves at that point.
    And The relation between Phase difference (Δϕ) and Path difference (Δx) is given as

    Δϕ=2πλΔx=kΔx

    where λ= wavelength of waves

 

 

Interference of light waves- 2

Principle of Super Position-

According to the principle of Super Position of waves, when two or more waves meet at a point, then the

resultant wave has a displacement (y) which is the algebraic sum of the displacements ( y1 and y2 ) of each wave.

 i.e y=y1+y2

consider two waves with the equations as

y1=A1sin(kxwt)y2=A2sin(kxwt+ϕ)

where ϕis the phase difference between waves y1 and y2.
And According to the principle of Super Position of waves

y=y1+y2=A1sin(kxwt)+A2sin(kxwt+ϕ)=A1sin(kxwt)+A2[sin(kxwt)cosϕ+sinϕcos(kxωt)]y=sin(kxwt)[A1+A2cosϕ]+A2sinϕcos(kxwt)(1)


Now let

Acosθ=A1+A2cosϕ and Asinθ=A2sinϕ


Putting this in equation (1) we get

y=Asin(kxωt)cosθ+Asinθcos(kxωt)
 

thus we get the equation of the resultant wave as

y=Asin(kxωt+θ)

where A= Resultant amplitude of two waves
and A=A12+A22+2A1A2cosϕ
and θ=tan1(A2sinϕA1+A2cosϕ)
where
A1= the amplitude of wave 1
A2= the amplitude of wave 2
- Amax=a1+a2 and Amin =a1a2

Resultant Intensity of two waves (I)-
Using IαA2
we get I=I1+I2+2I1I2cosϕ
where
I1= The intensity of wave 1
I2= The intensity of wave 2

  • . Imax=I1+I2+2I1I2Imax=(I1+I2)2
    . Imin =I1+I22I1I2Imin =(I1I2)2
    - For identical source-

    I1=I2=I0I=I0+I0+2I0I0cosϕ=4I0cos2ϕ2


    Average intensity : Iav=Imax+Imin2=I1+I2
    - The ratio of maximum and minimum intensities

    ImaxImin=(I1+I2I1I2)2=(I1/I2+1I1/I21)2=(a1+a2a1a2)2=(a1/a2+1a1/a21)2

    or

    I1I2=a1a2=(ImaxImin+1ImaxImin1)
     

Interference of Light-

It is of the following two types.

1. Constructive interference-

  • When the waves meet a point with the same phase, constructive interference is obtained at that point.

            i.e we will see bright fringe/spot.

  • - The phase difference between the waves at the point of observation is ϕ=0 or 2nπ
    - Path difference between the waves at the point of observation is Δx=nλ(i.e. even multiple of λ/2)
    - The resultant amplitude at the point of observation will be maximum

     i.e Amax=a1+a2


    If a1=a2=a0Amax=2a0
    - Resultant intensity at the point of observation will be maximum

     i.e Imax=I1+I2+2I1I2Imax=(I1+I2)2 If I1=I2=I0Imax=4I0
     

 

2. Destructive interference-

  • When the waves meet a point with the opposite phase, Destructive interference is obtained at that point.

            i.e we will see dark fringe/spot.

  • The phase difference between the waves at the point of observation is 

 

ϕ=180 or (2n1)π;n=1,2, or (2n+1)π;n=0,1,2

- Path difference between the waves at the point of observation is

Δx=(2n1)λ2( i.e. odd multiple of λ/2)

- The resultant amplitude at the point of observation will be maximum

 i.e Amin=a1a2


If a1=a2Amin =0
- Resultant intensity at the point of observation will be maximum

Imin=I1+I22I1I2Imin=(I1I2)2 If I1=I2=I0Imin=0
 

Study it with Videos

Interference of light waves- 1
Interference of light waves- 2

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