Class 12 Physics Nature and propagation of Light Notes

                                            

                             Wave Theory of Light

The light waves are electromagnetic waves which travel with different speed in different media. The wavelength of light wave is extremely small and it's wave properties are detected only under specialncircumstances. The microscopic phenomenon of light like interference diffraction and polarization are explained only by waves and cannot be explained by ray optics.

1. Huygen wave theory: The Dutch physicist Christian Huygen in 1690 suggested that light may be a wave nature. According to Huygens, Light was a longitudinal wave that travelled through material medium called ether. The ether was supposed to be massless, colourless invisible medium having an extremely high elasticity and practically no density. As light travels, ether vibrates. This theory is based on the fact that the speed of light must be less in denser medium. This was a very strong point in favour of the wave theory. The wave theory successfully explained many of the observed phenomena including the slower speed of light in denser medium. However, Huygen's wave theory couldnot prove the presence of ether.The difficulties in Huygen's theory were removed by young and Fresnel by assuming that light waves are transverse and not longitudinal as assumed by Huygen.

2. Electromagnetic Theory: In 1860, Maxwell gave the mathematical theory of electromagnetism which predicted the existence of electromagnetic wave propagating with speed of C = 3× 10 8 m/s where permeability of free space=4π×10 -7 H/m An electromagnetic wave consists of changing electric and magnetic fields. The two fields are perpendicular to each other fields are perpendicular to each other and to the direction of propagation of wave. Thus the light waves are transverse in nature. The electromagnetic wave can propagate through space even in the absence of any material medium.

3. Quantum Theory: In 1905 Einstein proposed a new theory of light called quantum theory, in order to explain the wave phenomena. According to quantum theory, light is transmitted as tiny bundles of energy called photons. A photon is considered to be massless bundles of electromagnetic energy. The energy E of a photodepends upon it's frequency 'ν'(new) and is given by E= hν=hf Where, h= Plancks constant= 6.62×10 -34 Js

4. Dual nature of Light: Some experiments shows that light behave like a wave and others indicate that it has a particle like nature.These two theories seem to be opposite in character but both have shown to have validity.Thus the light can exist in particle form as well as wave form.

Wave front: A source of light sends out disturbance in all direction. In a homogeneous medium, the velocity of light is the same in all direction. Therefore, all the particles of the medium at the same distance from the source of light vibrate in the same phase. The locus of all such particles vibrating in the same phase formed the wave front.

Thus, the wave front is defined as the locus of all the particles of the medium vibrating in the same phase.The lines perpendicular to the wave front give the direction of propagation of wave and are called rays.Let the point source S of light sending out spherical waves concentric with the source. Each arc represents a surface over which the phase of the wave is constant because each point on thesurface is at the same distance from the source. Such a surface of constant phase is the wave front.The lines perpendicular to the wave front are called rays.

At very large distance from the source the rays are nearly parallel and the wave fronts are then plane.Light from the sun reaches the earth in plane wave front.

Types of wave front:

Depending upon the shape of the source of light, the wave front can be divided into three types :

1. Spherical Wave front: When the source of light is a point source, the wave front is spherical with centre at the source because locus of all such points is equidistant from the point source is a sphere.

2. Cylindrical Wave front: When the source of light is linear such as slit, all the points equidistant from the linear source lie on the surface of a cylinder and such wave front is called cylindrical wave front.

3. Plane wave front: At very large distance from a source of any kind, the radius of curvature becomes very large. So that wave front will appear plane and such a wave front is called plane wave front.

Huygens Principle:

Huygens principle is a geometrical construction for determining the position of new wavefront at some instant from the position of the previous wave front. This principle can be stated as.

i. Every point on a given wave front acts as a source of secondary wavelets (called Secondary Wave) which travel in all directions with the velocity of light in the medium.

ii. The position of the new wave front at any instant is a surface touching these secondary wavelets tangentially in the forward direction at that instant.

Let us illustrate this principle by the following example.

Explanation:

Let us consider a diverging spherical wave moving through a medium as shown in figure. At

t=o, the spherical wave front has the position AB. We are able to find the position of the new

wave front after time t;. According to Huygens construction, each point on the wave front

AB acts as a source of secondary wavelets (only four points 1, 2, 3 and 4 are shown). Using

these points as source of secondary wavelets, draw circles of radius C × t where, C is the

velocity of light. These spherical surface represents the secondary wavelets after time t. Draw

a surface A l B l touching tangentially all the secondary wavelets in the forward direction then

the surface A l B l is the position of the new wavefront.

Laws of Reflection on the basis of wave theory                                                    

Let us consider a plane wave front AB incident on the plane mirror XY at an angle of incidence i as shown in fig. Both the wave front and mirror surface being perpendicular to the plane of paper. Now I 1, I 2 and I 3 are corresponding rays perpendicular to the wave front AB. According to Huygen Principle, every point on the wave front AB is a source of Secondary wavelets. Let the wave front is in contact with the surface XY at point A, at time t=0. Let the secondary wavelets from B strike XY at point A  in time t than B A = C × t where C is the velocity of light.In time t the secondary wavelet from A will travel a distance C × t above XY because XY is areflecting surface. With A as centre and C× t as radius, draw an arc B than B A = C×t.

From point A draw a plane tangent to secondary wavelet B  than A & B is the reflected wavefront.Similarly, the wavelet from C reach point D and from D reach point C ' in time t. The reflected rays must be perpendicular to the reflected wave front and are represented by rays R 1 R 2 and R 3 .

Let AN and A ' N' be normal drawn to the reflecting surface XY and 'r' be the angle of reflection.Since the angle between two straight lines is equal to the angle between their normals.

So  ABA' = i and  B'A'A = r

Where, i and r are angle made by incident wavefront AB and reflected wave front A ' B ' with the surface XY respectively.In right angled triangle ∆ABA ' and ∆A B ' A'

BAA ' = A B ' A ' [both being 90 0 C]

A B ' = BA ' = C × t

AA ' = AA ' (Common Side)

Hence, ∆ABA ' and ∆A B ' A ' are congruent triangle.

 BAA ' =  B' A ' A

i = r

Thus angle of incidence is equal to angle of reflection.

Laws of Refraction:

Let us consider a plane surface XY that separates a rarer medium 1 (i.e. air) from a denser medium 2

as shown in fig. If C is the velocity of light in the rarer medium and V is the velocity of light in the

denser medium then by definition refractive index of denser medium w.r. to rarer medium is

l  2 =

Suppose a plane wave front AB is incident on XY at an angle of incidence i as shown in figure. Now

I 1 I 2 and I 3 are corresponding incident rays perpendicular to wave front AB. According to Huygen's

principle, every point on the wave front AB is a source of secondary wavelets. Let the wave front is in

contact with the surface XY at point A in time t=0. Let the secondary wavelet from B strike the

surface XY at point A l in time 't'. than,

BA l = C × t

During this time the secondary wavelet from A will travel a distance V × t in the denser medium.

With A as centre and V × t as a radius draw an arc B l . From point A l , draw a plane tangent to the

secondary wavelet B l . Than A l B l is the refracted wave front. Similarly the wavelets from C reach

point D and from D reach point C l in time t. The refracted rays must be perpendicular to the refracted

wave front and are represented by rays R 1 R 2 and R 3 .

Let AN be normal drawn to the refracting surface at A and 'r' be the angle of refraction which the

refracted wave front A l B l makes with surface XY. i.e  A A l B l = r.

Similarly, the angle of incidence is the angle between incident wave front AB and the surface XY. i.e

 BAA l = i.

In right angled triangle ∆ABA l

sin i = = …………… (1)

Similarly In right angled triangle ∆A B l A l

sin r = = …………….. (2)

Thus = =

 = =

This proves the snells law.

Again incident wave front AB, the refracted wave front A l B l and the refracting surface XY areperpendicular to the plane of paper.

Q. The refractive index of diamond for yellow light of wavelength 539nm is 2.41. What is                      the velocity of light in diamond? (Velocity of light in vacuum or air(c ) =3×10 8 m/sec.

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