Wave optics

• What is diffraction?

  The bending of light at the edges of an obstacle in its path and entering into a region where shadows are expected on the basis of geometrical optics is known as diffraction.
• What is the corpuscular theory of Newton?

  1. Light travels in form of small particles known as corpuscles.
  2. Corpuscles are hard, elastic and massless.
  3. A source of light emits these corpuscles which travel along a straight line in absence of any external force.
  4. Speed of light in denser medium is greater than the speed of light in rarer medium.
  5. Different colours of light is because of different size of corpuscles.
  6. Speed of corpuscles is so high that there is almost no effect of gravity on them and hence they travel in a straight line which explains the rectilinear motion of light.
• Demerits of Newton's corpuscular theory:

  1. It could not explain the simultaneous reflection refraction of light, interference, diffraction, polarization and double refraction.
  2. If the particles were to be emitted from a source than a continuous decrease in the mass of source should have been observed which was not observed.
  3. It was later proved that the speed of light in rarer medium is greater than the speed of light and denser medium.
• Wave nature by huygens:

  1. Huygen proposed that light travels in form of longitudinal wave.
  2. Different colours of light is due to the different wavelengths of light.
  3. These waves are emitted from a source and travel with a uniform velocity in a homogeneous medium.
  4. Light travels in a medium known as luminiferous ether.
  5. This medium is present in vacuum as well.
• Demerits of huygens wave theory:

  1. It was later proved by Michelson and Morley that there is no medium such as luminiferous ether.
  2. It could not explain the rectilinear motion of light and polarization.
  3. Some effects such as photoelectric effect and compton effect could not be explained by this theory.
• Electromagnetic theory of light:

  
• Huygen's theory:

  • Primary source of light: sources that emit light of their own. (Sun, bulb)
  • Secondary source of light: sources that do not produce light of their own but receive light from some other source and either reflect or scatter it around. (Moon, planets, animals)
• What is a Wavefront?

  The locus of all points having the same phase at a given instant of time.
• What are the three types of wavefront?

  1. Spherical wavefront- a wavefront originating from a point source of light at a finite distance.
  2. Cylindrical wavefront- wavefront originating from a linear source of light at a finite distance.
  3. Plane wavefront- a wavefront originating from point source and linear source of light at an infinite distance.
• Huygens principle:

  He assumed light to be a wave.

  Each point on a wavefront acts as a secondary source of light and emits secondary light waves known as wavelets. The new wavefront can be obtained by taking the envelope of the secondary wavelets in forward direction. The wavelets travelling in backward direction are in ineffective.
• • Prove the reflection of light at a plane surface:

  Draw the diagram and prove it by RHS congruency that [i=r].

  • Prove the refraction of light at a plane boundary between two media:

  Draw the diagram and use snell's law to prove by v1/v2.
• Frequency of a wave is its fundamental property and does not change while going from one medium to another but the speed and wavelength of a wave do change and are inversely proportional to the relative refractive index of the second medium with respect to first.
• What is polarization?

  Restricting the vibrations of an unpolarized light in only one plane and removing the vibrations of other plane.
• Intensity is directly proportional to (amplitude)².
• Intensity of an unpolarized wave reduces by half after passing through a polarizer.
• Malus law:

  Malus' law gives the intensity of linearly polarized light wave after passes through a polarizer.

  
• What is brewster's law?

  • When a light is incident at an angle of incidence equal to polarizing angle, refractive index is numerically equal to the tangent of polarizing angle.
  • Brewster's angle is the angle of incidence for which reflected ray and refracted Ray are perpendicular.
• The Brewster's angle is the angle of incidence at which the refracted and reflected rays are perpendicular to each other
• According to the law of refraction, n₁ sin 0 = n₂ sin 0₂, which combined with the relationship for the Brewster's angle gives 0₁ = tan⁻¹ (n₂/n₁)
• Derive the expression for brewsters angle:

  
• Polarization by scattering:

  When sunlight strikes air molecules or dust particles in the atmosphere, it changes its direction this is called scattering.

  Polarization depends on the angle of scattering that is the angle between the direction of light incident on the molecule or dust particle and the direction of scattered light.

  If this angle is 90 degree then scattered light is plane polarized.
• What is interference?

  The enhancement or cancellation of displacement of light waves on their superposition is known as interference.
• What is constructive interference?

  On superposition of light waves, when the crest of one wave coincides with the crest of other wave and trough of one way coincides with the trough of another wave then the amplitude is doubled.

  A= a¹+a²

  What is destructive interference?

  On superposition of light waves, When the crest of one wave coincides with the trough of other then the displacement is zero.

  A=a¹-a²
• What are coherent sources of light?

  Sources which emit waves of the same frequency having a constant phase difference independent of time are called coherent sources.
• Conditions for obtaining well defined and steady interference pattern​:

  1. The two sources of light should be coherent.
  2. Two sources of light must be monochromatic.
  3. The two interfering waves must have same amplitude.
  4. Separation between the two slits must be small in comparison to the distance between plane containing slits and the observing screen.
  5. Two slits should be narrow.
  6. The two waves should be in the same state of polarization.
• Methods for obtaining coherent sources:

  1. Lloyd's mirror:

  • Monochromatic light from a source falls at a grazing angle on a plane mirror
  • Some light directly falls on the screen and some light after reflection
  • Reflected light appears to be coming from a virtual source, resulting in two coherent sources derived from a single source

  2. Fresnel biprism:

  • A biprism is a prism of vertex angle near 180°, made up of two prisms with a small refracting angle ranging from 30' to 1°
  • In the experimental arrangement, monochromatic light from a source falls on the biprism
  • The two halves of the biprism form virtual images as S1 and S2, which are coherent sources obtained from a single secondary source S