# Physics – Wave Theory of Light Textual Questions

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#### 1.1 Brief account of Huygen’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.

#### 2.1 Definition of Wave Surface:

• The surface of a sphere with source as a centre and distance travelled by a light wave as a radius where each wave arrives simultaneously is called wave surface.

#### 2.2 Definition of 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.

#### 2.3 Definition of 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.

#### 3.1 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.

#### 3.2 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.

#### 3.3 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.

#### 4.1 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.

#### 5.1 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.

#### 6.1 Polarization of Light:

• The phenomenon of restriction of the vibrations of light waves in a particular plane particular plane perpendicular to the direction of propagation of wave motion is called polarization of light.

#### 6.2 Distinguishing between Polarized Light and Unpolarized Light:

 Polarized Light Unpolarized Light When the vibrations of electric vectors are confined in one plane, the light is called plane polarized light. The wave in which the electric vector can vibrate in any plane (infinite possibilities) which is perpendicular to the direction of propagation of the wave is called unpolarized light. The x– and y– components of the electric field have a constant phase difference between them. The phase difference between the components of the electric field does not exist, and the changes in the electric field take place at random speeds. Can be obtained from sunlight Can be obtained by reflection and scattering Cannot be converted intp unpolarized light Can be converted into polarized light with the decrease in the intensity.

#### 7.1 The Plane of Polarization and the Plane of Vibration:

• The plane in which the vibration of polarized light takes place is called the plane of vibration.
• The plane perpendicular to the plane of vibration in which there are no vibrations of polarized light is called the plane of polarization and the light is said to be polarized in it.

#### 8.1 Brewster’s Law:

• The tangent of the polarising angle is equal to the refractive index of the refracting medium at which partial reflection takes place.

#### 8.2 To prove that at the polarizing angle the reflected ray and refracted ray are mutually perpendicular.

ip = angle of incidence and r = angle of refraction

#### 9.1 Doppler Effect in Light:

• The apparent change in the frequency of the light observed by an observer, due to relative motion between the source of the light and the observer, is called the Doppler effect.
• One major difference between Doppler effect exhibited by sound and light is as follows. In the case of sound, the frequency change depends on whether the source is moving or the observer is moving even if their relative velocities are the same. In the case of light, the Doppler effect depends only on the relative velocity of the source and the observer, irrespective of which of the two is moving. Hence the Doppler effect exhibited by light is symmetric.

Red Shift and Blue Shift of Light:

• When the source and observer move away from each other, the wavelength in the middle of the spectrum will be shifted towards red. This phenomenon is called red shift due to Doppler effect. When the source and observer move away from each other, the observer observes the lower frequency than the actual frequency of the light (towards red).
• When the source and observer move towards each other, the wavelength in the middle of the spectrum will be shifted towards blue. This phenomenon is called blue shift due to Doppler effect. When the source and observer move towards each other, the observer observes the higher frequency than the actual frequency of the light (towards blue).
• The measurement of Doppler shift helps in the study of motions of stars and galaxies.
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