Wave Optics:
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Questions and Answers

What does Huygens' Principle state about wavefronts?

  • Each point on a wavefront creates secondary wavelets. (correct)
  • Only the leading edge of a wavefront propagates.
  • Wavefronts do not contribute to interference patterns.
  • Wavefronts can only be plane or cylindrical.

    • In Young's Double-Slit Experiment, what path difference results in constructive interference?

  • Path difference = nλ (correct)
  • Path difference = (n-1)λ
  • Path difference = (n+1/2)λ
  • Path difference = λ/2

    • Which type of wavefront is produced by a point source?

  • Plane Wavefront
  • Linear Wavefront
  • Spherical Wavefront (correct)
  • Cylindrical Wavefront

    • What is the formula for fringe width in Young's Double-Slit Experiment?

    <p>β = λD/d</p> Signup and view all the answers

    Which condition leads to destructive interference in thin films?

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

    What characterizes Fresnel diffraction?

    <p>Source or screen is near the slit.</p> Signup and view all the answers

    In single-slit diffraction, what describes the central maximum?

    <p>It has the widest intensity distribution.</p> Signup and view all the answers

    What best defines spatial coherence?

    <p>Consistency of phase across the wavefront.</p> Signup and view all the answers

    What condition must be met for a minimum to occur in a single-slit diffraction pattern?

    <p>a sin θ = mλ</p> Signup and view all the answers

    How is the width of the central maximum in a single-slit diffraction pattern approximately calculated?

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

    Which equation represents the grating condition for constructive interference?

    <p>d sin θ = nλ</p> Signup and view all the answers

    What is the formula for the resolving power of a microscope?

    <p>R = (2n sin θ)/λ</p> Signup and view all the answers

    In Malus' Law, how is the intensity of polarized light I related to the angle θ when passing through an analyzer?

    <p>I = I0 cos^2 θ</p> Signup and view all the answers

    What does the grating equation $d \sin \theta = n \lambda$ represent in the context of diffraction grating?

    <p>The relationship between grating spacing and wavelength</p> Signup and view all the answers

    Which method is used to achieve polarization through scattering?

    <p>Scattering in the atmosphere</p> Signup and view all the answers

    Which law relates intensity to the angle of polarization in light?

    <p>Malus' Law</p> Signup and view all the answers

    According to the Rayleigh Criterion, when can two sources be considered resolved?

    <p>When the first minimum coincides with the maximum of the other</p> Signup and view all the answers

    What is represented by the formula $R = \frac{2n\sin \theta}{\lambda}$?

    <p>The resolving power of a microscope</p> Signup and view all the answers

    What does Brewster's Law describe?

    <p>The angle at which light reflects off a surface</p> Signup and view all the answers

    Which of the following statements about polarization is incorrect?

    <p>Polarization can only be achieved through reflection.</p> Signup and view all the answers

    In the context of telescope resolving power, what does the formula $R = \frac{D}{1.22 \lambda}$ indicate?

    <p>The diameter of the telescope's objective lens.</p> Signup and view all the answers

    What does Huygens' Principle state about wavefronts?

    <p>Each point on a wavefront serves as a source of secondary wavelets.</p> Signup and view all the answers

    In the context of reflection, what is true about the angles involved?

    <p>The angle of incidence equals the angle of reflection.</p> Signup and view all the answers

    What condition must be met for constructive interference to occur in the Young's Double-Slit Experiment?

    <p>Path difference must equal nλ.</p> Signup and view all the answers

    What is the derived formula for the fringe width (β) in Young's Double-Slit Experiment?

    <p>β = λDd.</p> Signup and view all the answers

    What does Snell's Law relate to in terms of wave behavior?

    <p>It relates the refractive indices to the angles of incidence and refraction.</p> Signup and view all the answers

    When light travels from medium 1 to medium 2, what happens to its speed?

    <p>It decreases if medium 2 has a lower refractive index.</p> Signup and view all the answers

    What is the path difference formula for thin film interference?

    <p>Path difference = 2μt cos r.</p> Signup and view all the answers

    What type of fringe occurs when the path difference equals (n + 1/2)λ?

    <p>Destructive interference.</p> Signup and view all the answers

    Study Notes

    Huygens' Principle and Wavefronts

    • Huygens' Principle states that every point on a wavefront acts as a source of secondary spherical wavelets that spread out.
    • The new wavefront is the tangential surface to these secondary wavelets.
    • Types of wavefronts:
      • Plane: Produced by sources at infinite distances
      • Spherical: Produced by a point source
      • Cylindrical: Produced by a linear source
    • Huygens' principle explains reflection, refraction, and diffraction.

    Interference of Light

    • Principle of Superposition: Amplitudes of overlapping light waves add up.
    • Types of Interference:
      • Constructive: Crest meets crest (bright fringe), path difference = nλ.
      • Destructive: Crest meets trough (dark fringe), path difference = (n+1/2)λ.

    Young’s Double-Slit Experiment

    • Fringe Width (β): Distance between two consecutive bright or dark fringes, β=λD/d.
    • Coherence:
      • Temporal: Consistency of phase over time.
      • Spatial: Consistency of phase across the wavefront.

    Thin Film Interference

    • Interference in thin films is caused by reflections from the upper and lower surfaces.
    • Conditions for Interference:
      • Constructive: 2μtcos⁡r=nλ.
      • Destructive: 2μtcos⁡r=(2n+1)λ/2.
    • Examples: Colors in soap bubbles, anti-reflective coatings.

    Diffraction of Light

    • Types of Diffraction:
      • Fresnel: Source or screen close to the slit.
      • Fraunhofer: Source and screen at infinite distances, producing parallel rays.

    Single-Slit Diffraction

    • Central Maximum: Brightest fringe, width 2θ (where θ≈λ/a).
    • Intensity Pattern: Maximum at the center, decreasing towards edges.

    Diffraction Grating

    • Grating Equation: dsin⁡θ=nλ.
    • Applications: Spectroscopy and wavelength measurement.

    Polarization of Light

    • Unpolarized Light: Vibrations in all directions perpendicular to propagation.
    • Polarization Methods:
      • Reflection: Partial polarization upon reflection.
      • Refraction: Birefringent materials split light into two polarized rays.
      • Scattering: Polarization occurs when light scatters in the atmosphere.
    • Malus' Law: I=I0cos⁡2θ.
    • Brewster’s Law: tan⁡θB=n.

    Resolving Power of Optical Instruments

    • Rayleigh Criterion: Two sources are resolved if the first minimum of one diffraction pattern coincides with the maximum of the other.
    • Microscope Resolving Power: R=2nsin⁡θ/λ.
    • Telescope Resolving Power: R=D/1.22λ.
    • Applications: Designing lenses and optical instruments with higher precision.

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