MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Wave Theory of Light Page 1

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 1. Early Theories of Light The earliest theories put forward to explain the nature of light. i) Newton's Corpuscular Theory ii) Huygen's Wave Theory Newton's Corpuscular Theory This theory is based on the assumption that light consists of minute, weightless particles called 'corpuscles'. The properties of the corpuscles are: The corpuscles travel with great speed. The corpuscles travel in straight lines in a given time. When the corpuscles enter the eyes of the observer, a sensation of light is produced. Corpuscles of different masses and sizes give rise to different colours. Reflection is explained on the basis of repulsion of corpuscles from the reflecting surface. Refraction is explained on the assumption that refracting surfaces attract the corpuscles. Drawbacks of Newton's Theory There is no change in mass of the source due to emission of material particles, viz corpuscles. The phenomenon of simultaneous reflection and refraction of light from transparent surfaces could not be accounted for. According to Newton's theory, the velocity of light in a denser medium turns out to be greater than the velocity of light in a rarer medium. Experimentally, the converse is found to be true. Many other phenomena like interference, diffraction, polarization, etc. could not be explained on the basis of Newton's corpuscular theory. Huygen's Wave Theory According to Huygen's theory, light propagates in the form of waves. For the propagation of a wave, Huygen's assumed the existence of the medium called Ether. The waves of light are emitted by the source of light and they travel in straight lines. The different colours of light are due to the different wavelengths of the light waves. The phenomena of reflection, refraction, interference, diffraction, etc. could be explained. Drawbacks Many phenomena in Modern Physics such as Photo-electric effect, Compton effect, etc. could not be explained by wave theory. The propagation of waves through vacuum could not be accounted for, hence a hypothetical medium called ether was assumed to be present. However, the presence of ether could not be detected. It was experimentally shown that medium like ether does not exist.

2.

Wave Front, Wave Normal

Wave surface: A wave surface at any instant is defined as the locus of all the points of the medium to which the waves reach at that instant and are in the same phase.

• For a point source of light 'O', light waves are emitted in all directions.
• If velocity of light (in air) = c
Distance covered in time
t = ct

Therefore, at the end of time t, light waves from 'O', will reach the surface of a sphere of radius ct, with centre at O.

• This spherical surface is a wave surface.
• All points on the surface of the sphere are in the same phase. They are in the same state of vibration.

Wave front: A part of the wave surface is a wave front. The three kinds of wave front are:
i) Spherical wave front
ii) Plane wave front and
iii) Cylindrical wave front

Spherical wave front is a wave front originating from a point source.

Plane wave front: If the point source of light is at a very large distance, the radius of the spherical wave front is very large and a small part of this wave front can be considered to be a plane wave front. E.g. light from the sun reaches the earth in the form of plane wave fronts.

Cylindrical wave front: If the source of light is in the form of a narrow slit, the wave front originating from it has the shape of a cylinder. This is called a Cylindrical wave front.

Wave normal: A line perpendicular to the surface of the wave front.
In case of homogeneous media, the wave normal is a ray of light.

The rays of light are shown by arrows. A point source of light gives a divergent beam of rays.
The rays corresponding to a plane wave front form a parallel beam of rays.

3.

Huygen's Principle and Construction of Wave Fronts

Huygen's Principle:

• Every point on a wave front acts as a secondary source and emits secondary waves in all directions but effective only in the forward direction.
• The envelope of the secondary wave fronts at any later instant is the new wave front at that instant.

Huygen's Construction: The progress of a wave front can be studied with the help of a geometrical construction suggested by Huygen's. If the nature of a wave front at any instant is known, its nature and position at any later instant can be determined.

Huygen's Construction of a Spherical Wave Front

O: Point source of light in the air
c: Velocity of light in the air
ct: distance covered in time t
ABC: Section of spherical wave front at time
t with centre at O and radius ct
A, B, C: Points on primary wave front which behave like a secondary source
A1, B1, C1: Points on spherical wave front with centres at A, B, C respectively and radius
c dt
Surface A1 B1 C1: New wave front at time
t + dt

Huygen's Construction of Plane Wave Front

ABC: Section of plane wave front at an instant t
A, B, C: Points on primary wave front which behave like a secondary source
A1, B1, C1: Points on plane wave front with centres at A, B, C. respectively and radius
cdt
Surface A1 B1 C1: New plane wave front at time
t + dt.

Note: Secondary wave fronts travelling in backward direction do not exist.

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