Physics: Interference of Light
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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.

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

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