Physics: Interference of Light
50 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the condition for the nth order principal maximum in the grating spectrum?

  • (a + b) sin θ = mλ
  • a sin θ = nλ
  • a sin θ = mλ
  • (a + b) sin θ = nλ (correct)

    • What happens when the two conditions given by equation (2) are simultaneously satisfied?

  • The resultant intensity will be maximum.
  • The grating spectrum gives us a maximum every slit by itself.
  • The grating spectrum becomes invisible.
  • The direction in which the grating spectrum should give us a maximum every slit by itself will produce darkness in that direction. (correct)

    • What is the condition for the absent spectra in the diffraction pattern?

  • a sin θ = mλ
  • (a + b) sin θ = nλ
  • (a + b) /a = n/m (correct)
  • (a + b) sin θ = mλ

    • What happens when a = b?

    <p>The 2nd, 4th, 6th, etc. orders of the spectra will be absent.</p> Signup and view all the answers

    What happens when b = 2a?

    <p>The 3rd, 6th, 9th, etc. orders of the spectra will be absent.</p> Signup and view all the answers

    How can the number of spectra visible in a given grating be calculated?

    <p>With the help of the equation n = (a + b) sin θ / λ</p> Signup and view all the answers

    What is the maximum possible value of the angle of diffraction?

    <p>90°</p> Signup and view all the answers

    What is the grating element equal to?

    <p>2.54 N cm, N being the number of lines per inch in the grating</p> Signup and view all the answers

    What is the condition for n max if (a + b) is between λ and 2λ?

    <p>n max = (a + b) / λ</p> Signup and view all the answers

    What is the physical significance of the absent spectra in the diffraction pattern?

    <p>The direction in which the grating spectrum should give us a maximum every slit by itself will produce darkness in that direction.</p> Signup and view all the answers

    What is the fundamental requirement to get a well-defined interference pattern?

    <p>Constant phase difference between the two waves</p> Signup and view all the answers

    What type of coherence is a measure of phase relation between the waves reaching at two different points in space at the same time?

    <p>Spatial coherence</p> Signup and view all the answers

    What is the name of the experiment that demonstrates temporal coherence?

    <p>Michelson-Morley experiment</p> Signup and view all the answers

    What is the purpose of dividing the wave front in interference experiments?

    <p>To produce interference of light from a single source</p> Signup and view all the answers

    What is the characteristic of coherent sources?

    <p>They emit light waves of same frequency and amplitude</p> Signup and view all the answers

    What is the advantage of using two virtual sources formed from a single source?

    <p>They can act as coherent sources</p> Signup and view all the answers

    What is the reason for using a broad source in an interference pattern experiment?

    <p>To observe the whole interference pattern</p> Signup and view all the answers

    What is the shape of the air film formed in Newton's Ring Experiment?

    <p>Wedge-shaped</p> Signup and view all the answers

    What is the condition for constructive interference in a wedge-shaped thin film?

    <p>2µcos (r + θ) = (2n + 1) λ/2</p> Signup and view all the answers

    What is the phenomenon of bending of light around the corners of an obstacle and their spreading into the geometrical shadow?

    <p>Diffraction</p> Signup and view all the answers

    What is the type of diffraction where the incident wave front is plane?

    <p>Fraunhofer's diffraction</p> Signup and view all the answers

    What is the condition for the central fringe to be dark in Newton's Ring Experiment?

    <p>2 µt = λ/2</p> Signup and view all the answers

    What is the path difference between the rays emanating from extreme points A and B of the slit AB?

    <p>πa sinθ / λ</p> Signup and view all the answers

    What is the condition for the maximum value of resultant amplitude R at point C?

    <p>α = 0</p> Signup and view all the answers

    What is the direction of the secondary maxima in the diffraction pattern?

    <p>tanα = n</p> Signup and view all the answers

    What is the resultant amplitude at a point P on the screen in the case of Fraunhofer's diffraction at a double slit?

    <p>R cos(φ/2)</p> Signup and view all the answers

    What is the path difference between the two rays AB and DE in the case of reflected light in a thin film?

    <p>2 µt Cos r - λ/2</p> Signup and view all the answers

    What is the phase difference between the two waves originating from S1 and S2 in the case of Fraunhofer's diffraction at a double slit?

    <p>φ = 2πb sinθ / λ</p> Signup and view all the answers

    What is the characteristic of the diffraction pattern obtained on the screen in the case of Fraunhofer's diffraction at a double slit?

    <p>Equally spaced interference maxima and minima</p> Signup and view all the answers

    What is the condition for constructive interference in the case of reflected light in a thin film?

    <p>2 µt Cos r = n λ</p> Signup and view all the answers

    What is the difference between the conditions of maxima and minima in reflected and transmitted light in a thin film?

    <p>The conditions are opposite in both cases</p> Signup and view all the answers

    What happens when white light is incident on a thin film?

    <p>Only a few wavelengths satisfy the condition of maxima</p> Signup and view all the answers

    What happens when either the thickness of the film or the angle of incidence is varied?

    <p>A different set of colours is observed</p> Signup and view all the answers

    What is the reason for the colouration of a thin film?

    <p>Due to the interference of light in the film</p> Signup and view all the answers

    What is the purpose of drawing fine, equidistant, and parallel lines on an optically plane glass plate?

    <p>To create a grating for diffraction of visible light</p> Signup and view all the answers

    What is the effect of increasing the number of slits (N) in a plane diffraction grating?

    <p>The intensity of principal maxima increases</p> Signup and view all the answers

    What is the path difference between the waves originating from two consecutive slits in a plane diffraction grating?

    <p>(a+b) sin θ</p> Signup and view all the answers

    What is the resultant amplitude due to all waves diffracted from each slit in a direction θ?

    <p>R sin α</p> Signup and view all the answers

    What is the phase difference between the waves from two consecutive slits in a plane diffraction grating?

    <p>2π/λ(a+b) sin θ</p> Signup and view all the answers

    Why are photographic reproductions of gratings used in practice?

    <p>Because they are less expensive than original gratings</p> Signup and view all the answers

    What is the number of minima between two successive principal maxima?

    <p>(N - 1)</p> Signup and view all the answers

    What is the condition for the first order principal maximum?

    <p>m = N</p> Signup and view all the answers

    What is the condition for the nth order principal maximum in the direction of diffraction θ?

    <p>(a + b) sin θ = nλ</p> Signup and view all the answers

    What is the physical significance of the central principal maximum?

    <p>Direction of maximum intensity</p> Signup and view all the answers

    What is the number of secondary maxima between two successive principal maxima?

    <p>(N - 2)</p> Signup and view all the answers

    What is the condition for the absent spectra in the diffraction pattern when a = b?

    <p>n = 2m</p> Signup and view all the answers

    What is the maximum possible value of the angle of diffraction?

    <p>90°</p> Signup and view all the answers

    What is the condition for the nth order principal maximum when b = 2a?

    <p>n = 3m</p> Signup and view all the answers

    What is the significance of the equation (a + b) sin θ = nλ?

    <p>It gives the condition for the nth order principal maximum</p> Signup and view all the answers

    What is the number of equispaced minima between zero and first order maxima?

    <p>(N - 1)</p> Signup and view all the answers

    Study Notes

    Here are the study notes in detailed bullet points, focusing on key facts with context:

    • Coherent Sources*
    • Two sources are said to be coherent if they emit light waves of the same frequency, nearly the same amplitude, and are always in phase with each other.
    • There are two types of coherence:
      • Temporal coherence (Coherence in time): a measure of phase relation of a wave reaching at given points at two different times.
      • Spatial coherence (Coherence in space): a measure of phase relation between the waves reaching at two different points in space at the same time.
    • Interference*
    • Interference occurs when two or more waves superimpose on each other.
    • Methods for producing interference patterns:
      • Division of wave front: interference of light takes place between waves from two sources formed due to a single source.
      • Division of amplitude: interference takes place between the waves from the real source and virtual source.
    • Interference in Thin Film*
    • An optical medium of thickness in the range of 0.5 μm to 10 μm may be considered as a thin film.
    • Interference can take place in a thin film by:
      • Reflected light
      • Transmitted light
    • Conditions for constructive and destructive interference:
      • Constructive interference: path difference = even multiple of λ/2
      • Destructive interference: path difference = odd multiple of λ/2
    • Colors of thin films: only few wavelengths will satisfy the condition of maxima, and corresponding colors will be seen in the pattern.
    • Necessity of Broad Source or Extended Source*
    • A broad source is necessary to see the whole interference pattern.
    • Interference Due to Non-uniform Thin Film (Wedge-shaped Thin Film)*
    • Path difference: Δ = 2µt cos (r+θ) - λ/2
    • Conditions for maxima and minima:
      • Constructive interference: 2µt cos (r+θ) = (2n + 1) λ/2
      • Destructive interference: 2µt cos (r+θ) = nλ
    • Newton's Ring Experiment*
    • Newton's rings: a special case of interference in a film of variable thickness, such as that formed between a plane glass plate and a convex lens in contact with it.
    • Experimental arrangement: a monochromatic light source, a lens, a glass plate, and a plano-convex lens.
    • Path difference: Δ = 2µt - λ/2
    • Conditions for maxima and minima:
      • Constructive interference: 2µt = (2n + 1) λ/2
      • Destructive interference: 2µt = nλ
    • Diameter of bright and dark rings:
      • Bright rings: Dn = √(2λR) √(2n + 1)
      • Dark rings: Dn = √(4nλR)
    • Applications of Newton's Rings*
    • Measurement of wavelength of sodium light by Newton's rings.
    • Measurement of refractive index of a liquid by Newton's rings.
    • Diffraction*
    • The phenomenon of bending of light around the corners of an obstacle and their spreading into the geometrical shadow of an object.
    • Diffraction pattern: a distribution of light intensity resulting in dark and bright fringes.
    • Types of diffraction:
      • Fresnel's diffraction: source of light or screen or both are at a finite distance from the diffracting element.
      • Fraunhofer's diffraction: both the source and the screen are effectively at infinite distance from the diffracting element.
    • Fraunhofer Diffraction at a Single Slit*
    • Conditions for maxima and minima:
      • Principal maximum (central maxima): α = 0
      • Minima: sin α = 0 => α = ±nπ, where n = 1, 2, 3, ...
      • Secondary maxima: α = ±(2n + 1) π/2, where n = 1, 2, 3, ...
    • Intensity distribution:
      • Intensity of central maxima: I = I0
      • Intensity of first secondary maxima: I1 = I0 / 22
      • Intensity of second secondary maxima: I2 = I0 / 62
    • Fraunhofer Diffraction at a Double Slit*
    • Diffraction pattern: a number of equally spaced interference maxima and minima.
    • Resultant amplitude: due to the interference between the two waves of same amplitude and a phase difference φ originating from the middle points of the two slits.### Fraunhofer's Diffraction at a Double Slit
    • The resultant intensity at a point on the screen due to a double slit is given by I = 4A^2 cos^2 β / α^2
    • The intensity depends on two factors:
      • sin^2 α / α^2, which gives the diffraction pattern due to each single slit
      • cos^2 β, which gives the interference pattern due to two waves of same amplitude (R) originating from the mid-points of their respective slits

    Position of Maxima and Minima

    • Principal maxima are given by A^2 / α^2, θ = 0
    • Position of minima are given by sin α = 0, α ≠ 0, which implies α = ±mπ, where m = 1, 2, 3, ...
    • Position of secondary maxima approach to α = ±3π/2, ±5π/2, ±7π/2, ...

    Interference Term

    • I is maximum when cos^2 β = 1, which implies β = ±nπ, where n = 0, 1, 2, 3, ...
    • Intensity is minimum when cos^2 β = 0, which implies β = (2n+1)π/2

    Plane Transmission Diffraction Grating (N-Slits Diffraction/Diffraction due to double slits)

    • A plane diffraction grating is an arrangement of a large number of close, parallel, straight, transparent, and equidistant slits, each of equal width a, with neighboring slits being separated by an opaque region of width b.
    • The spacing (a + b) between adjacent slits is called the diffraction element or grating element.

    Theory of Grating

    • The diffraction pattern obtained on the screen with a very large number of slits consists of extremely sharp principal interference maximum, while the intensity of secondary maxima becomes negligibly small.
    • If we increase the number of slits (N), the intensity of principal maxima increases.
    • According to Huygen's principle, all points within each slit become the source of secondary wavelets, which spread out in all directions.
    • The resultant amplitude R due to all waves diffracted from each slit in the direction θ is given by R = A sin α, where A is a constant and α = πa sinθ / λ.

    Resultant Amplitude and Intensity

    • The resultant amplitude R' in the direction θ is given by R' = R sin Nβ / sin β
    • The corresponding intensity at P is given by I = R'^2 = A^2 sin^2 α / α^2 sin^2 Nβ / sin^2 β

    Principal Maxima, Minima, and Secondary Maxima

    • The condition for principal maxima is sin β = 0, i.e., β = ±nπ, where n = 0, 1, 2, 3, ...
    • The condition for minima is sin Nβ = 0, but sin β ≠ 0
    • The intensity of secondary maxima is proportional to N^2 /[1+(N^2-1) sin^2 β], whereas the intensity of principal maxima is proportional to N^2.

    Absent Spectra with a Diffraction Grating

    • It may be possible that while the first order spectra is clearly visible, second order may not be visible at all, and the third order may again be visible.
    • The condition for the absent spectra is given by (a+ b) /a = n/m, where a is the width of the transparent portion and b is the width of the opaque portion.

    Number of Orders of Spectra with a Grating

    • The number of spectra that are visible in a given grating can be easily calculated with the help of the equation n = (a+b) sin θ / λ
    • The maximum possible value of the angle of diffraction θ is 90°, and therefore sin θ = 1.

    Interference

    • Coherent sources: two sources emitting light waves of the same frequency, nearly the same amplitude, and always in phase with each other.
      • Temporal coherence (longitudinal coherence): phase relation of a wave at a given point at two different times.
      • Spatial coherence (transverse coherence): phase relation between waves at two different points in space at the same time.
    • Methods for producing interference patterns:
      • Division of wavefront: interference between waves from two sources formed from a single source.
      • Division of amplitude: interference between the waves from the real source and virtual source.

    Interference in Thin Films

    • Thin film: an optical medium of thickness in the range of 0.5 μm to 10 μm.
    • Interference in a thin film occurs due to:
      • Reflected light
      • Transmitted light
    • Condition for constructive interference: 2 µt cos r = n λ (reflected light) 2 µt cos r = n λ (transmitted light)
    • Condition for destructive interference: 2 µt cos r = (2n + 1) λ/2 (reflected light) 2 µt cos r = (2n + 1) λ/2 (transmitted light)
    • Colours of thin films: depend on the thickness of the film and the angle of incidence.

    Interference Due to Non-Uniform Thin Films (Wedge Shaped Thin Films)

    • Condition for constructive interference: 2µcos (r + θ) = (2n + 1) λ/2
    • Condition for destructive interference: 2µcos (r + θ) = nλ

    Newton's Ring Experiment

    • Newton's rings: a special case of interference in a film of variable thickness.
    • Experimental arrangement: extended source of light, lens, glass plate, and plano-convex lens.
    • Condition for constructive interference: 2 µt = (2n + 1) λ/2
    • Condition for destructive interference: 2 µt = nλ

    Diffraction

    • The phenomenon of bending of light around the corners of an obstacle and their spreading into the geometrical shadow.
    • Types of diffraction:
      • Fresnel's diffraction: source of light or screen or both are at a finite distance from the diffracting element.
      • Fraunhofer's diffraction: both the source and the screen are at an infinite distance from the diffracting element.

    Fraunhofer's Diffraction at a Single Slit

    • Experimental arrangement: source of light, collimating lens, slit, converging lens, and screen.
    • Condition for maxima: α = 0 or θ = 0
    • Condition for minima: sin α = 0
    • Position of minima: α = nπ

    Fraunhofer's Diffraction at a Double Slit

    • Experimental arrangement: source of light, collimating lens, two parallel slits, converging lens, and screen.
    • Condition for maxima: R = 2A sin(πa sinθ/λ)
    • Condition for minima: sin(πa sinθ/λ) = 0

    Plane Transmission Diffraction Grating (N-Slits Diffraction/Diffraction due to Double Slits)

    • A plane diffraction grating consists of a large number of close, parallel, straight, transparent, and equidistant slits.
    • Condition for principal maxima: a sin θ = nλ
    • Condition for minima: sin(2β) = 0
    • Positions of secondary maxima: between two successive principal maxima.

    Absent Spectra with a Diffraction Grating

    • Condition for absent spectra: a sin θ = mλ (a + b) sin θ = nλ

    • Absent spectra occur when the conditions for single-slit pattern and grating spectrum are simultaneously satisfied.### Conditions for Absent Spectra

    • The condition for absent spectra in the diffraction pattern is (a+b)/a = n/m.

    • When the width of the transparent portion is equal to the width of the opaque portion (a = b), the condition becomes n = 2m, resulting in the absence of 2nd, 4th, 6th, etc. orders of the spectra.

    • When b = 2a, the condition becomes n = 3m, resulting in the absence of 3rd, 6th, 9th, etc. orders of the spectra.

    Number of Orders of Spectra with a Grating

    • The equation to calculate the number of visible spectra in a grating is (a+b) sin θ = n λ.
    • The grating element (a+b) is equal to 1/N, where N is the number of lines per inch in the grating.
    • The maximum possible value of the angle of diffraction θ is 90°, so sin θ = 1.
    • The maximum possible order of spectra (n max) is equal to (a+b)/λ.
    • If the grating element (a+b) is between λ and 2λ, then n max is determined by the equation (a+b)/λ.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Understanding the principles of interference in light waves, including coherent sources and phase differences.

    More Like This

    Unleash Your Understanding of Light Interference and Diffraction
    15 questions

    Unleash Your Understanding of Light Interference and Diffraction

    AccomplishedBixbite avatar
    AccomplishedBixbite
    Interference Patterns in Optics Quiz
    8 questions

    Interference Patterns in Optics Quiz

    UnaffectedUvarovite avatar
    UnaffectedUvarovite
    Wave Optics
    30 questions

    Wave Optics

    NourishingRoseQuartz avatar
    NourishingRoseQuartz
    Physics Chapter 27: Wave Optics
    43 questions

    Physics Chapter 27: Wave Optics

    WittyVision4473 avatar
    WittyVision4473
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser