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Wave Optics
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Nature of Light:1. Corpuscular theory of light (Newton, 1675):
➢ Every source of light emits large numbers of tiny, perfectly elastic, rigid, and
weightless particles known as corpuscles in a medium surrounding the source.
➢ Corpuscles always travel in a straight line in all directions and carry kinetic energy
with it.
➢ The corpuscles travel faster in the denser medium than in rarer medium.
➢ The different colors of light have different sizes of the corpuscles.
➢ Reflection occurs due to elastic collision of corpuscles with the reflecting surface.
➢ Refraction occurs because corpuscles are attracted by the particles of the medium
Failures of corpuscular theory
➢ Assumption that light travels faster in the denser medium than in the rarer medium
which has been proved wrong.
➢ The assumption that the different colors of light are due to the differences in the sizes
of corpuscles has no justification.
➢ Newton assumed that reflection of light is due to the repulsion between the corpuscles
and reflecting surface while refraction of light is due to the attraction between the
corpuscles and refracting surface. Thus, a medium could either attract or repel the
corpuscles of light. But we know that glass partially reflects and partially refracts
light. So, glass can’t attract and repel the corpuscles of light simultaneously.
➢ Can’t explain the phenomena of diffraction, interference, and polarization of light.
2. Wave theory of light (Huygens, 1678):
➢ Light is a mechanical longitudinal wave which travels with uniform velocity in
homogeneous medium.
➢ Different colours are due to different wavelengths of light waves.
➢ To explain the propagation of waves of light through vacuum, Huygen suggested the
existence of a hypothetical all-pervading medium called luminiferous ether. It is very
dilute (zero density), highly elastic and transparent medium.
, Advantages of wave theory
➢ Interference, diffraction, refraction, reflection, simultaneous refraction and reflection,
double refraction can be explained.
➢ According To Huygens, theory the velocity of light in denser medium is less than
velocity of light in a rarer medium as was experimentally proved by Foucault.
Failures of wave theory
➢ Could not explain polarization and quantum mechanical phenomena of light including
photoelectric effect, Compton effect, Raman effect.
➢ Michelson and Morley experiment concluded that luminiferous ether does not exist.
➢ Light is not a mechanical longitudinal wave.
Wavefront: The continuous locus of all points of a wave in the same phase.
Types of Wavefronts:
a) Spherical wavefront: When wave travels in all direction from a point source
b) Cylindrical wavefront: When wave travels from a linear source
c) Plane wavefront: A small portion of a spherical/cylindrical wavefront coming from a
large distance can be assumed as a plane wavefront.
Ray of Light: An arrow drawn perpendicular to the wavefront in the direction of propagation
of wave.
a) Rays are perpendicular to the wavefronts.
b) The time taken for light to travel from one wavefront to another is the same along
any ray.
Beam of Light: A group of parallel rays.
Huygens’s Principle of Secondary Wavelets:
1. Each point on a wavefront acts as a fresh source of secondary disturbance which emits
secondary wavelets that spread out in all directions with the speed of light in the given
medium.
2. The new wavefront at any later time is given by the forward envelop of the secondary
wavelets at that time.
Huygens’s Construction: It is a geometrical method of determining position and shape of the
new wavefront at a later time.
, 1. Let 𝐴𝐴′ be the position of a wavefront (plane/spherical), moving towards right, at any
instant of time.
2. Each point on 𝐴𝐴′ acts as secondary disturbance which travels with same speed c. To
draw the new wavefront after time t, spheres of radii ct are drawn from each point on
𝐴𝐴′ .
3. The energy flows from 𝐴𝐴′ to 𝐵𝐵′ along rays ⊥ to 𝐴𝐴′ and 𝐵𝐵 ′ . This energy
propagation is maximum in the forward direction and zero in the backward direction.
So backward wavefront doesn’t exist.
REFLECTION ON THE BASIS OF HUYGEN’S WAVE THEORY:
AB=incident wavefront, XY= reflecting surface
AB touches XY at B and then at successive points towards C.
If t = time taken for the secondary
wavelets to grow from B to D with
speed c, ⇒ 𝐵𝐷 = 𝑐𝑡.
The reflected wavefront is the tangent
CD drawn to the hemisphere of radius
ct drawn from B. Here, BD=AC=ct.
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