#### Assumptions of Newton’s Corpuscular Theory of Light:

• Every source of light emits a large number of tiny particles known as corpuscles in a medium surrounding the source.
• These corpuscles are perfectly elastic, rigid and weightless.
• The corpuscles travel in a straight line with very high speeds, which are different in different media.
• Explanation of Sensation of Vision When corpuscles fall on the retina of the eye, they produce the sensation of vision.
• The different colours of light are due to the different sizes of the Corpuscles.

#### Drawbacks of Newton’s Corpuscular Theory of Light:

• The corpuscular theory fails to explain partial reflection and refraction at the surface of transparent media.
• It fails to explain the phenomenon like interference, polarization and diffraction of light.
• The theory predicted that the velocity of light is more in the optically denser medium than that in rarer medium. Foucault’s experimental observation disproved it.
• As Corpuscles were assumed as particles, there should be a continuous decrease in the mass of a source which emits light continuously for a long time. There was no experimental evidence for it.

#### Maxwell’s Electromagnetic Theory:

• Maxwell proposed the existence of electromagnetic waves. He obtained a relation between magnetism and electricity.
• He assumed light to be in the form of electromagnetic waves due to the fact that the velocity of electromagnetic waves is equal to that of light.
• He observed that the electromagnetic waves do not require any medium for their propagation hence they can travel through a vacuum. Thus the propagation of light in a vacuum can be explained by assuming them to be electromagnetic waves.

#### Max Planck’s Quantum Theory:

• To explain black body radiations Max Planck proposed this theory. He proposed that the light is propagated in the form of light energy called quanta or photon.
• Each photon or quanta has energy given by E = h υ. Where ‘h’ is Planck’s constant and ‘υ’ is the frequency of the photon.

#### Max Planck’s Quantum Theory:

• To explain black body radiations Max Planck proposed this theory.
• He proposed that the light is propagated in the form of light energy called quanta or photon.
• Each photon or quanta has energy given by E = h υ. Where ‘h’ is Planck’s constant and ‘υ’ is the frequency of the photon.

#### Huygens’s Wave Theory of Light:

• According to wave theory, light from a source is propagated in the form of longitudinal waves with uniform velocity in a homogeneous medium. (Later it was proved that the light waves are transverse waves).
• Different colours of light are due to different wavelengths of the light waves.
• When light enters our eyes we get the sensation of light.
• To explain the propagation of light through the vacuum, Huygens assumed the existence of a hypothetical (imaginary) elastic medium called luminiferous ether.  According to Huygens, ether particles are all-pervading (present everywhere) and possess properties such as inertia, zero density and perfect transparency.

#### Merits of Huygens’s Wave Theory of Light:

• On the basis of wave theory, the phenomenon of reflection, refraction, diffraction, interference, and total internal reflection of light could be explained.
• Wave theory correctly predicted that velocity of light in an optically denser medium is less than that in a rarer medium which is in agreement with experimental results.

#### Demerits of Huygens’s Wave Theory of Light:

• Wave theory assumes the existence of luminiferous ether. However, experimental attempts to detect the presence of ether particle were unsuccessful.
• Huygen’s theory could not explain the rectilinear propagation of light.
• The phenomena of the photoelectric effect, Crompton effect in Modern Physics and polarization cannot be explained using wave theory.

#### Wavefront:

• A  locus of all the points of a medium, to which light waves reach simultaneously so that all these points are in the same phase is called wavefront.

#### Wave Normal:

• A perpendicular drawn to the surface of a wavefront at any point in the direction of propagation of light is called as Wave Normal.

#### Ray of Light :

• The direction in which light is propagated is called a ray of light.

#### Spherical Wavefront:

• Consider a point source of light S placed in air.  The source will emit waves of light in all possible directions. If the velocity of light in air is c, then in time ‘t’, each wave will cover a distance ct. Therefore, at the end of the time interval ‘t’  the light emitted, by, the source will reach at all points as a sphere with centre S and radius equal to ct.
• All the points on the surface of this sphere are in the same phase.  Such a spherical wave surface of the sphere is called spherical. wavefront.
• A spherical wavefront is given by a point source. A line source gives a cylindrical wavefront. When the radius of a spherical wavefront is a very large small portion of the wavefront can be considered as a plane wavefront.

#### Huygen’s principle:

• Every point on a wavefront behaves as if it is a secondary source of light sending secondary waves in all possible directions.
• The new secondary wavelets are more effective in the forward direction only.
• The envelope (tangent) of all the secondary wavelets at a given instant in the forward direction gives the new wavefront at that instant.

#### Huygen’s Construction of Spherical Wavefront:

• Consider a point source O of light giving rise to a spherical wavefront ABCDE at any instant. According to Huygens’ principle, each point on a wavefront acts as a secondary source of light producing secondary wavelets in all directions.
• Let c be the velocity of light in air and ‘t’ be the time after which position of the wavefront is to be found. During time ‘t’ the light wave will travel a distance of ‘ct’. To find the position and shape of the wavefront after a time ‘t’, a number of spheroids of radius ‘ct’ are drawn with their centres A, B, C, D and E.
• The tangential spherical envelope (surface) joining the points A’, B’, C’, D’ and E’ in the forward direction is the new wavefront at that instant.
•  The secondary wavelets are effectively only in the direction of wave normal.  Therefore, a backward wavefront is absent.

#### Huygen’s Construction of Plane  Wavefront:

• Consider a plane wavefront ABCDE at any instant. According to Huygens’ principle, each point on a wavefront acts as a secondary source of light producing secondary wavelets in all directions.
• Let c be the velocity of light in air and ‘t’ be the time after which position of the wavefront is to be found. During time ‘t’ the light wave will travel a distance of ‘ct’. To find the position and shape of the wavefront after a time ‘t’, a number of spheroids of radius ‘ct’ are drawn with their centres A, B, C, D and E.
• The tangential envelope (surface) joining the points A’, B’, C’, D’ and E’ in the forward direction is the new wavefront at that instant.
• The secondary wavelets are effectively only in the direction of wave normal.  Therefore, a backward wavefront is absent.

### Reflection and Refraction of Light

#### Explanation of Reflection of Light From Plane Reflecting Surface on the Basis of Huygens’s Wave Theory of Light:

• Consider a plane wavefront bounded by parallel rays PA and QB, travelling through air be obliquely incident on a plane reflecting surface XY. At an instant when the plane wavefront AB just touches the reflecting surface, point A’ becomes a secondary source to send out backward secondary wavelets.
• As the incident plane, wavefront proceeds further let ‘t’ be the time required by end B of this wavefront to reach the reflecting surface at C. if ‘c’ is the velocity of light in the air then, BC = c t.
• During this time, the secondary wavelet, originating from point A spreads over, a hemisphere. In time ‘t’ the radius of this spherical wavelet is AD = c t
• Draw a tangent from point C to the secondary spherical wavelet to meet it at D. As C and D are in the same phase, the tangent CD represents the reflected plane wavefront after time ‘t’.
• From ray diagram:

∠ PA’N = ∠ BCN’ = i, angle of incidence

∠ B’CA’ = 90° – i ,

∠ NA’D =  r, angle of reflection

∠ DA’C = 90° – r

In Δ A’B’C and Δ CDA’

∠ A’B’C = ∠ A’DC  =  90° Angle between plane wavefront and wave normal

B’C = A’D = ct

A’C is common to both the triangles

Hence, A’B’C and DCDA’ are congruent. (Hypotenuse side theorem)

∠ B’CA’  = ∠ DA’C (CACT)

∴ 90° – i = 90° – r

∴        i = r

Thus the angle of incidence is equal to the angle of reflection,

• From the diagram, it can be seen that the incident ray and the reflected ray lie on either side of the normal at the point of incidence. Similarly the incident ray, the reflected ray and the normal at the point of incidence lie in the same plane i.e. plane of the paper. Hence laws of reflection are proved. Thus the phenomenon of reflection is explained on the basis of the Huygens’ wave theory of light.

#### Explanation of Refraction of Light From Plane Refracting Surface on the Basis of Huygens’s Wave Theory of Light:

• Consider a plane wavefront bounded by parallel rays PA and QB, travelling through a rarer medium of refractive index μ1 be obliquely incident on a plane refracting surface XY. At an instant when the plane wavefront AB just touches the refracting surface at point A’, point A’ becomes a secondary source to send out secondary wavelets in the second medium of refractive index μ2.
• As the incident plane, wavefront proceeds further let ‘t’ be the time required by end B of this wavefront to reach the reflecting surface at B’. if c1 is the velocity of light in the air then, B’C = c1 t.
• During this time, the secondary wavelet, originating from point A’ spreads over, a hemisphere in the second medium. Let c2 be the speed of the light in the second medium. In time ‘t’ the radius of this spherical wavelet is A’D = c2 t
• Draw a tangent from point C to the secondary spherical wavelet to meet it at D. As C and D are in the same phase, the tangent CD represents the refracted plane wavefront after time ‘t’.
• Construct NN’, normal to the refracting surface at A’.
• From ray diagram:

∠AA’N  +  ∠ NA’B’ =  90°    ……. (1)

∠NA’B’  + ∠ B’A’C =  90°    ……. (2)

From (1) & (2)

∠ AA’N  + ∠ NA’B’ = ∠ NA’B’ + ∠ B’A’C

∴ ∠ AA’N = ∠ B’A’C  =  i

∠N’A’D  +  ∠ DA’C =  90°    ….. (3)

∠DA’C  +  ∠ A’CD =  90°     …. (4)

From (3) & (4)

∠ N’A’D + ∠ DA’C = ∠ DA’C + ∠ A’CD

∴ ∠ N’A’D = ∠ A’CD =  r

∠ A’B’C = ∠ A’CD = 90°, (Angle between plane wavefront and wave normal)

• IThus Snell’s law is proved., From the diagram, it can be seen that the incident ray and the refracted ray lie on the opposite side of the normal at the point of incidence. Similarly the incident ray, the refracted ray and the normal at the point of incidence lie in the same plane i.e. plane of the paper. Hence laws of refraction are proved. Thus the phenomenon of refraction is explained on the basis of the Huygens’ wave theory of light.
• For an optically denser medium μ > 1, hence the velocity of light in an optically rarer medium is more than optically denser medium.