33Wave nature of Light

📚
WAVE NATURE OF LIGHT
▢ Main Phenomena:

Table 1: Interference vs Diffraction

Feature
Interference
Diffraction
Meaning
Redistribution of light energy due to superposition of coherent waves
Bending/spreading of light around obstacle or aperture
Common examples
Young's double slit interference, Newton's rings
Single slit diffraction, diffraction grating
Fringe width
Usually equal in YDSE
Central maximum is widest in single slit
Intensity
Bright fringes nearly equal if sources equal
Secondary maxima have decreasing intensity
▢ Young's Double Slit Experiment:
❖ Type: Interference
❖ Central Fringe: Central bright fringe / central maximum

Table 1: YDSE Symbols

Symbol
Meaning
\(D\)
Distance between slit and screen
\(d\)
Distance between two slits
\(\lambda\)
Wavelength of light
\(\beta\)
Fringe width
\(y_n\)
Position of nth fringe from central maximum

Table 2: YDSE Formulae

Quantity
Formula
Fringe width
\(\beta=\frac{\lambda D}{d}\)
Position of nth bright fringe
\(y_n=n\frac{\lambda D}{d}\)
Position of nth dark fringe
\(y_n=\left(n-\frac{1}{2}\right)\frac{\lambda D}{d}\)
Path difference for nth bright fringe
\(\Delta x_n=n\lambda\)
Path difference for nth dark fringe
\(\Delta x_n=\left(n-\frac{1}{2}\right)\lambda\)
Phase difference for nth bright fringe
\(\Delta\phi_n=2n\pi\)
Phase difference for nth dark fringe
\(\Delta\phi_n=\left(n-\frac{1}{2}\right)2\pi=(2n-1)\pi\)
❖ Conditions:

Table 1: Bright and Dark Fringe Conditions

Fringe
Path difference
Phase difference
Bright / constructive
\(n\lambda\)
\(2n\pi\)
Dark / destructive
\(\left(n-\frac{1}{2}\right)\lambda\)
\((2n-1)\pi\)
▢ Newton's Rings:
❖ Type: Interference in thin film
❖ Setup: Plano-convex lens placed on glass plate
❖ Central Ring in Reflected Light: Dark
❖ R: Radius of curvature of plano-convex lens

Table 1: Newton's Rings Formulae in Reflected Light

Ring
Radius
nth bright ring
\(r_n=\sqrt{\left(n-\frac{1}{2}\right)\lambda R}\)
nth dark ring
\(r_n=\sqrt{n\lambda R}\)
Central ring
Dark
❖ Important Point: In transmitted light, the ring system is complementary to reflected light
▢ Single Slit Diffraction:
❖ Type: Diffraction at single slit
❖ Central Maxima: Bright and widest

Table 1: Single Slit Symbols

Symbol
Meaning
\(D\)
Distance between slit and screen
\(d\)
Width of slit
\(\lambda\)
Wavelength of light
\(\beta_0\)
Width of central maximum
\(y_n\)
Position of nth band from central maximum

Table 2: Single Slit Diffraction Formulae

Quantity
Formula
Width of central maximum
\(\beta_0=\frac{2\lambda D}{d}\)
Width of secondary maximum
\(\beta=\frac{\lambda D}{d}\)
Width of secondary minimum
\(\beta=\frac{\lambda D}{d}\)
Position of nth dark fringe
\(y_n=n\frac{\lambda D}{d}\)
Approximate position of nth bright fringe
\(y_n=\left(n+\frac{1}{2}\right)\frac{\lambda D}{d}\)
❖ Important Points:
    ◈ _*type: bullet
  1. Central maximum width is twice the secondary maximum width
  2. Central maximum has maximum intensity
  3. Intensity of secondary maxima decreases on moving away from centre
▢ Diffraction Grating:
❖ Type: Diffraction by many equally spaced slits
❖ **table:
    ◈ caption: Symbols
    ◈ data:
      1. Symbol
      2. Meaning
      1. \(a\)
      2. Width of opaque portion
      1. \(b\)
      2. Width of transparent portion / slit width
      1. \(a+b\)
      2. Grating element
      1. \(\theta_n\)
      2. Angular position of nth order spectrum
      1. \(n\)
      2. Order of spectrum
      1. \(N\)
      2. Number of lines per inch
▢ Intensity in Interference:
❖ Basic Relation: \(I\propto A^2\)
❖ **table:
    ❖ For Equal Amplitudes:
      ◈ **type: bullet
    1. \(A_1=A_2\)
    2. \(A*{max}=2A\)
    3. \(A*{min}=0\)
    4. \(I*{min}=0\)
    ▢ Comparison of Formulae:

    Table 1: YDSE vs Single Slit vs Newton's Rings vs Grating

    Topic
    Bright / Maxima
    Dark / Minima
    YDSE
    \(y_n=n\frac{\lambda D}{d}\)
    \(y_n=\left(n-\frac{1}{2}\right)\frac{\lambda D}{d}\)
    Single slit
    \(y_n\approx\left(n+\frac{1}{2}\right)\frac{\lambda D}{d}\)
    \(y_n=n\frac{\lambda D}{d}\)
    Newton's rings
    \(r_n=\sqrt{\left(n-\frac{1}{2}\right)\lambda R}\)
    \(r_n=\sqrt{n\lambda R}\)
    Grating
    \((a+b)\sin\theta_n=n\lambda\)
    Missing orders possible by slit condition
    ▢ High-Yield Recall:

    Table 1: Wave Nature of Light One-Liners

    Fact
    Answer
    Wave nature phenomena
    Interference and diffraction
    YDSE
    Interference
    Newton's rings
    Interference
    Single slit
    Diffraction
    Grating
    Diffraction
    YDSE central fringe
    Bright
    Newton's ring central ring in reflected light
    Dark
    Single slit central maximum width
    \(\frac{2\lambda D}{d}\)
    Single slit secondary maximum width
    \(\frac{\lambda D}{d}\)
    YDSE fringe width
    \(\beta=\frac{\lambda D}{d}\)
    YDSE nth bright
    \(y_n=n\frac{\lambda D}{d}\)
    YDSE nth dark
    \(y_n=\left(n-\frac{1}{2}\right)\frac{\lambda D}{d}\)
    Newton's nth bright ring
    \(r_n=\sqrt{\left(n-\frac{1}{2}\right)\lambda R}\)
    Newton's nth dark ring
    \(r_n=\sqrt{n\lambda R}\)
    Grating equation
    \((a+b)\sin\theta_n=n\lambda\)
    Grating element
    \(a+b=\frac{2.54}{N}\ cm\)
    Bright fringe path difference
    \(n\lambda\)
    Dark fringe path difference
    \(\left(n-\frac{1}{2}\right)\lambda\)
    Bright fringe phase difference
    \(2n\pi\)
    Dark fringe phase difference
    \((2n-1)\pi\)
    Intensity-amplitude relation
    \(I\propto A^2\)
    Maximum amplitude
    \(A_1+A_2\)
    Minimum amplitude
    \(A_1-A_2\)
    Q1.
    The ratio of maximum to minimum intensities in Young's double slit interference is 16, then the ratio of their individual intensities is
    📅BP 2014
    Q2.
    Interference when two waves of intensities I1 and I2 differing in phase by φ are superimposed, the contrast will be maximum if
    📅BP 2014
    Q3.
    Which of the following doesn't explain wave theory of light
    📅BP 2014
    Q4.
    When a light ray is illuminated on a glass slab of refractive index 4/3, such that reflected ray is polarized, then angle made by the ray with the horizontal is:
    📅BP 2014/2017
    Q5.
    Two light rays having the same wavelength λ in vacuum are in phase initially. Then the first ray travels a path L1 through a medium of refractive index μ1, while the second ray travels a path of length L2 through a medium μ2. The two waves are then combined to observe interference. The phase difference between the two waves is
    📅
    Q6.
    What happens to the fringe pattern when Young's double slit experiment is performed in water instead of air?
    📅BP 2011
    Q7.
    A beam of light strikes on a thin soap bubble surface. After refraction the ray of light form interference pattern on the screen. If Δx and r is the path difference and angle of refraction then graph denoting their correct relation is:
    📅BP 2010
    Q8.
    Young's double slit experiment is made in liquid. The 10th bright fringe in liquid lies where 6th dark fringe lies in vacuum. The refractive index of the liquid is
    📅BP 2009
    Q9.
    In Young's double slit experiment, the separation of slit is 1.9 mm and fringe spacing is 0.31 mm at distance 1 m from the slit. The wavelength of light used is
    📅MOE 2014
    Q10.
    If the amplitude is in the ratio of 2:3 then intensity will be in the ratio of (given that frequency is same)
    📅MOE 2014
    Q11.
    Two waves each of loudness L superimpose to produce beats. The maximum loudness of the beats will be
    📅IOM 2014
    Q12.
    The polarizing angle between reflected and refracted rays is
    📅KU 2016
    Q13.
    In Young's double slit experiment, 12 fringes are obtained in a certain fragment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to 400 nm, number of fringes obtained in the same segment of the screen will be:
    📅IOM 2011
    Q14.
    The width of the third fringe in Young's double slit interference experiment is 0.1 mm. The width of the fifth fringe will be:
    📅MOE 2013
    Q15.
    Two coherent monochromatic light beams of intensities in the ratio 1:4 are superposed, the ratio of maximum to minimum possible intensities in the resulting beam is
    📅MOE 2010
    Q16.
    The fringe width in an interference pattern due to two coherent sources is
    📅MOE 2009
    Q17.
    In Young's experiment, one slit is covered with a transparent blue filter and the other is left as it is then the interference pattern
    📅KU 2014
    Q18.
    A laser produces
    📅KU 2014
    Q19.
    If maximum intensity is 16 times the minimum intensity then the ratio of their amplitudes will be:
    📅KU 2014
    Q20.
    Two waves are defined to be coherent if
    📅KU 2014
    Q21.
    The fact that light can be polarized establishes the light
    📅KU 2013, 2012, 2011, 2017
    Q22.
    In order to increase fringe width
    📅KU 2010
    Q23.
    In Young's double slit experiment fringe width is 2 mm. Separation between 9th bright fringe and 2nd dark fringe from the centre of the fringe system is:
    📅IE 2010
    Q24.
    Yellow light is used in a single slit diffraction experiment with a slit of width 0.6 mm. If yellow light is replaced by X-rays, the observed pattern will reveal that
    📅IE 2010
    Q25.
    A Young's double slit experiment having fringe width of 0.4 mm is immersed inside the water having μ = 4/3, The fringe width becomes:
    📅
    Q26.
    Sound quality of a portable radio is improved by adjusting the orientation of the aerial. Which statement is a correct explanation of this improvement?
    📅KU 2013, 2012
    Q27.
    Unusual coloration seen in oil drops is due to
    📅KU 2010
    Q28.
    A radar sends a signal of frequency 7.8×109/s towards aeroplane moving with certain velocity. A frequency difference of 2.7×103/s is reflected from aeroplane. Find the velocity of aeroplane.
    📅IOM 07
    Q29.
    The fringe width of interference pattern of monochromatic light produced by double slit experiment is β. The wavelength of light is λ. Then the ratio of the slit separation to the distance of the slits and the screen is:
    📅IOM 2063
    Q30.
    A beam of light is passed through two parallelly placed tourmaline plates. Now when one of the plate is rotated, brightness is changed due to:
    📅IOM 98
    Q31.
    If Young's experiment is performed inside water, the fringe width will:
    📅IOM 98
    Q32.
    The wave nature of matter is not apparent to our daily observations because the magnitude of the associated wavelength of the object is:
    📅IOM 98
    Q33.
    In a diffraction experiment a plane transmission grating having 5500 lines/cm is illuminated by a source of light of wavelength 6000 Angstrom. Number of maxima observed on the screen will be:
    📅MOE Curriculum
    Q34.
    Fringe width between two consecutive fringes is 1.78×10-4 m and the slit separation is 0.1 mm. If the distance between screen and slit is 0.2 m then wavelength of light used is:
    📅MOE 2008
    Q35.
    Two waves of the same wavelength and amplitude interfere to produce a minimum when their phase difference is:
    📅MOE 2065
    Q36.
    Two waves are represented as: y1 = 20 sin 70 and y2 = 40 sin 100. The ratio of intensities is given by
    📅MOE 2063
    Q37.
    Which of the following is the most appropriate?
    📅MOE 2061
    Q38.
    The frequency of radiowaves is 15 MHz. What is its wavelength?
    📅MOE 2056
    Q39.
    In an interference pattern minima are obtained when phase difference between interfering waves is:
    📅MOE 2055
    Q40.
    Young's experiment is performed inside water, the fringe width will:
    📅MOE 2055
    Q41.
    Phase difference between 2 waves y1 = a sin ωt and y2 = b cos ωt is given by:
    📅MOE 2054
    Q42.
    Interference pattern is not produced by:
    📅IE-05
    Q43.
    Diffraction isn't seen in case:
    📅IE-06
    Q44.
    In a double slit diffraction, central bright fringe is obtained if path difference is multiple of:
    📅IE-06
    Q45.
    Coherent light waves never arises from:
    📅IE-07
    Q46.
    In a single slit diffraction:
    📅IE-08
    Q47.
    In an interference pattern produced by two identical coherent sources of monochromatic light, the intensity at the site of central maxima is I. The new intensity of central maxima when one of the slits is closed is:
    📅
    Q48.
    In a diffraction experiment using light of wavelength λ, d is the separation between the slits, D is distance of screen from slits. For what value of D, width of central maxima is equal to d?
    📅
    Q49.
    Interference occurs mostly due to:
    📅IE-01
    Q50.
    Sky appear blue due to:
    📅IE-02
    Q51.
    If two waves of same amplitude A but having different frequencies interfere, then:
    📅
    Q52.
    The ratio of amplitudes of two coherent sources is 1:2 then the ratio of maximum and minimum interference intensity fringe is:
    📅IE-03
    Q53.
    Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio.
    📅BPKIHS-95
    Q54.
    Soap bubble shines in different colours due to:
    📅BPKIHS 98
    Q55.
    In Young's double slit interference experiment if the slit separation is made 3 folds, the fringe width becomes.
    📅BPKIHS 2000
    Q56.
    The intensity ratio at a point of observation due to two coherent waves is 100:1. The ratio between their amplitudes is:
    📅
    Q57.
    Two coherent sources whose intensity ratio is 81:1 produce interference fringes. The ratio of maximum to minimum intensity in the fringe system is
    📅
    Q58.
    In the Young's double slit experiment, if the widths of the slits are in the ratio 4:9, the ratio of the intensity at maxima to the intensity at minima will be
    📅
    Q59.
    An interference pattern is observed by Young's double slit experiment. If now the separation between the coherent sources is halved and the distance of screen from coherent source is double, the fringe width:
    📅
    Q60.
    Fringe width observed in Young's double slit experiment is β. If the frequency of the source is doubled, the fringe width become/remain
    📅
    Q61.
    A beam of electron is used in Young's double slit experiment. When the velocity of electron is increased then
    📅
    Q62.
    In Young's double slit experiment, if the width of 2nd fringe is 10-2 cm, then the width of 4th fringe will be
    📅
    Q63.
    In Young's double slit experiment, the fringe width is found to be 0.4mm. If the whole apparatus is immersed in water of refractive index 4/3 without disturbing the geometrical arrangement, the new fringe width will be
    📅
    Q64.
    In Young's double slit experiment, the fifth maximum with wavelength λ1 is at a distance d1 and the same maxima with wavelength λ2 is at a distance d2. Then d1/d2 is equal to
    📅
    Q65.
    Two light waves of wavelength λ1 and λ2 become incident simultaneously on double slits in Young's interference experiment. If 3rd bright fringe of wavelength λ1 meets 4th bright fringe of wavelength λ2, then
    📅
    Q66.
    In Young's experiment, one slit is covered with a blue filter and the other with a yellow filter. Then the interference pattern
    📅
    Q67.
    The two coherent sources with intensity ratio B produce interference. The fringe visibility will be:
    📅
    Q68.
    In a Young's double slit experiment, the distance between two slits is (1/2)×10-3 m. The distance between slit and screen is 25 cm. If wavelength of light used is 5000 Å then the angular thickness of fifth dark fringe is
    📅
    Q69.
    The distance between two slits is 1 mm are illuminated with a light of wavelength 6×10-7 m. The distance between slit and screen is 1 m. Then the separation between 3rd dark and 5th bright fringe is:
    📅
    Q70.
    In Young's double slit experiment the two slits act as coherent sources of equal amplitude a and of wavelength λ. In another experiment with the same set-up the two slits are sources of equal amplitude a and wavelength λ, but are incoherent. The ratio of intensity of light at the midpoint of the screen in the first case to that in the second case is:
    📅
    Q71.
    In Young's experiment the wavelength of red light is 7800 Å and that the blue light is 5200 Å. The value of 'n' for which (n+1)th blue band coincides with nth red band is:
    📅
    Q72.
    In a certain region A and B in thin film we get 10 fringes in the reflected beam of wavelength λ = 4600 Å. How many fringes will be observed in the same region with λ = 6571 Å
    📅
    Q73.
    In a biprism experiment the wavelength of monochromatic light used is 6000 Å. The distance between the two virtual sources is 6 mm. The number of fringes formed per mm on a screen placed 1 m away is:
    📅
    Q74.
    A thin sheet of glass (μ = 1.5) of thickness 6 microns introduced in the path of one of interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. Then the wavelength of light used is
    📅
    Q75.
    Light of wavelength 6000 Å is reflected at nearly normal incidence from a soap film of refractive index 1.4. The least thickness of the film that will appear black is
    📅
    Q76.
    In Young's experiment, we get 10 fringes in the field of view of monochromatic light of wavelength 4000 Å. If we use monochromatic light of wavelength 5000 Å then the number of fringes obtained in the same field of view is
    📅
    Q77.
    The central bright fringe of the interference pattern produced by light of wavelength 6000 Å is shifted to the position of fifth bright fringe by introducing a thin glass plate of refractive index 1.5. Then the thickness of the glass plate is
    📅
    Q78.
    In Young's double slit experiment, the distance between two sources is 0.1 mm. The distance of the screen from the source is 20 cm. Wavelength of light used is 5460 Å. The angular position of the first dark fringe is
    📅
    Q79.
    In Young's double slit experiment, the two equally bright slits are coherent, but of phase difference π/3. If maximum intensity on the screen is I0, the intensity at the point on the screen equidistant from the slit is
    📅
    Q80.
    In Young's double-slit experiment the aperture screen distance is 2 m. The fringe width is 1 mm. If a thin plate of glass (μ=1.5) of thickness 0.006 mm is placed over one of the slits, then there will be a lateral displacement of fringe by
    📅
    Q81.
    A diffraction pattern is obtained using a beam of red light. What happens if the red light is replaced by blue light?
    📅
    Q82.
    A parallel beam of light of wavelength 5000 Å is incident normally in a single slit of width 0.001 mm. The light is focused by a convex lens on a screen placed in focal plane. The first minimum is formed for the angle of diffraction equal to
    📅
    Q83.
    A beam of light of wavelength 600 nm from distant source falls on a single slit 1.0 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the fifth dark fringes on either side of the central bright fringe is:
    📅
    Q84.
    Light of wavelength 6328 Å is incident on a slit having width of 0.2 mm. The width of central maxima, measured from minimum to minimum of the diffraction pattern on a screen 9 m away will be about:
    📅
    Q85.
    A slit of width 12×10-7 m is illuminated by light of wavelength 6000 Å. The angular width of the central maxima is approximately..
    📅
    Q86.
    A slit of width d is placed in front of a lens of focal length 0.5 m and illuminated normally with light of wavelength 5.89×10-7 m. The first diffraction minima on either side of the central diffraction maxima are separated by 2×10-3 m. The width of the slit is
    📅
    Q87.
    A parallel beam of monochromatic light is incident normally on a slit. The diffraction pattern is observed on a screen placed at the focal plane of a convex lens. If the slit width is increased, the central maximum of the diffraction pattern will become
    📅
    Q88.
    Find the angle of diffraction for first order secondary minima if wavelength of light used is 550 nm and slit of width 0.55 mm
    📅
    Q89.
    The first diffraction minimum due to a single slit diffraction is at 30° for a light of wavelength λ. If the width of slit is 1.0 μm, the wavelength λ is:
    📅
    Q90.
    Fraunhofer diffraction experiment at a single slit using light of wavelength 400 nm, the first minimum is formed at an angle of 30°. Then the direction θ of the first secondary maximum is given by:
    📅
    Q91.
    In a single slit diffraction experiment, the width of the slit is made double the original width. If I0 is the intensity of the principal maximum, then the new intensity will be
    📅
    Q92.
    Light of wavelength λ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at distance D. The linear width of the principal maximum is equal to the width of the slit if D equals:
    📅
    Q93.
    An unpolarised light wave is travelling along positive X-axis. The electric field vector in the beam vibrates in the direction
    📅
    Q94.
    An unpolarised beam of intensity I0 falls on a polaroid. The intensity of emergent light is
    📅
    Q95.
    An unpolarised beam of intensity I0 is incident on a pair of Nicols making an angle 60° with each other. The intensity of light emerging from the pair is
    📅
    Q96.
    Ordinary light incident on a glass slab at the polarising angle is refracted in glass and suffers a deviation of 22°. The value of the angle of refraction in glass in this case is
    📅
    Q97.
    An unpolarised light of amplitude a is incident on polariser then amplitude of polarised light emerging from polariser is
    Q98.
    A ray of light strikes a glass plate at an angle of 60°. If the reflected and refracted rays are perpendicular to each other, the index of refraction of glass is
    📅
    Q99.
    Two Nicols are oriented with their principal plans making an angle of 60°. Then the percentage of incident unpolarised light which passes through the system is
    📅
    Q100.
    A ray of light from a denser medium strikes a rarer medium so that the reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are r and r' respectively. Then critical angle would be:
    📅
    Q101.
    When a monochromatic light passes in Young's Double slit experiment then the resultant interference fringe is:
    📅KU 2016
    Q102.
    Soap bubbles shine due to
    📅IOM 2016
    Q103.
    Two waves are coherent if they:
    📅KU 2017
    Q104.
    The light waves from two lamps cannot produce interference pattern on screen because:
    📅KU 2017
    Q105.
    In Young's double slits experiment, when red light is replaced by violet then
    📅IOM 2017