Wave Optics -:
Learning objectives
-: Electromagnetic waves, Plane waves.
-: Velocity of electromagnetic waves.
-: Properties of electromagnetic waves.
-: Hertz experiment.
-: Electromagnetic spectrum.
-: Huygen's wave theory, Huygen's principle, explanation of reflection and refraction.
-: Interference, Young's double slit experiment, Lloyd's single mirror, Fresnel's bi-prism experiment.
1. ELECTROMAGNETIC WAVES
James Clerk Maxwell, one of the pioneers in the field of electromagnetic waves, gave his theory of electromagnetic waves in 1865. An electromagnetic wave is composed of oscillating electric and magnetic fields which oscillate in manually perpendicular planes. These two planes, besides being perpendicular to each other, are also perpendicular to the direction of propagation of the wave. Using his equations, called Maxwell's equations , he derived the formula for speed of electromagnetic waves in a medium. Using this formula, the speed of light in air or vaccum was calculated to be 2.99792 × 10⁸ m s-¹ which, we all know, is accurately the speed of light.
Maxwell's idea was new in 1865. It was only in 1887 that his theory was put on sound footings by the famous Hertz experiment. Using this set up, Hertz was able to generate electromagnetic waves. These waves didn't lie in visible region of spectrum. They lay in short wave region of radio waves. This experiment was a pioneer effort in its direction. Using this experiment as base, Jagdish Chandra Bose generated waves in the infra-red region. Marconi, also, gave significant contribution to the field of communication using electromagnetic waves.
2. PLANE ELECTROMAGNETIC WAVES
A plane electromagnetic wave is a wave which travels in x direction and has electric and magnetic fields along y and z directions respectively. In reality, the wave is not in this simplified form. The plane electromagnetic wave has electric and magnetic fields lying in manually perpendicular planes which are also perpendicular to the direction of propagation of wave. The number of such planes in infinite. So, there are infinite possible directions of electric and magnetic fields as shown in [ ].
By using Maxwell equations, we can obtain following relations between Ey and Bz.
3. PROPERTIES OF ELECTROMAGNETIC WAVES
All the properties of electromagnetic waves which we have studied till now are summarized as follows :
1. They consist of oscillating magnetic field and electric field at right angle to each other.
2. Electric and magnetic fields are in phase with each other.
3. They do not require a material medium for their propagation.
4. They travel with velocity 1/√μ⁰€⁰ through air or vaccum and with velocity 1/√μ€ through any other medium.
5. Since electric and magnetic fields, both obey the principle of superposition, the electromagnetic waves will also obey this principle.
4. OSCILLATORY DISCHARGE
Oscillations of charge in an electric circuit can be understood by the following simple experiment.
Consider two sphere S and S′ charged oppositely say S positively and S′ negatively. Electric lines of force will be as shown in [Fig.17.3(a)]. Let these spheres be connected by means of conducting wire. Current flows from S to S′. This results in collapsing of electric lines of force and developing of circular magnetic lines of force around the wire. The growth of magnetic lines of force is maximum when the current in the wire is maximum and the electric lines of force have completely disappeared [Fig. 17.3(b)]. Now the magnetic lines of force begin to collapse upon the wire, and an e.m.f. is set up in the wire which keeps the current flowing in same direction. As a result of this, sphere S′ gets charged positively and S negatively. Consequently electric lines of force, as shown in Fig.17.3(c), are produced. These oscillations continue till whole of the energy is dissipated against the resistance of the circuit. The amount of charge decreases gradually as shown in Fig.17.4. These oscillations are called damped oscillations .
5. HERTZ EXPERIMENT
In 1888, a young German scientist "Heinrich Hertz" not only succeeded in producing electromagnetic waves but was able to detect them also. The scheme of his experiment is given below :
The apparatus consists of two metalic spheres S and S′ capable of being slided along two rods R and R′ having a spark gap P in between [Fig.17.5]. The two rods R and R′ are connected to the two terminals of the secondary of an induction coil. The receiving system also consists of a circular wire having a park gap Q in between.
The spheres S and S′ get charged oppositely due to impulse of an e.m.f. from the induction coil. The charge starts oscillating, producing series of sparks across P. This results in radiation of energy in the form of electromagnetic waves. These radiations are received by the circuit Q. For a proper tuning, it can be seen that a spark appears across Q also.
6. HUYGEN'S WAVE THEORY
Huygen, a Dutch mathematician, in 1678, gave a theory regarding nature of light. The theory popularly known as Huygen's wave theory . According to this theory, light is a sort of disturbance. The particles of the medium, vibrate in a direction, at right angle to the direction of propagation of disturbance. The process is called wave-motion . Considering light to be a wave-motion, following properties of light could be explained :
1. Rectilinear propagation of light 2. Reflection
3. Refraction 4. Interference 5. Diffraction
6. Polarization.
Photoelectric effect could not be explained on the basis of this theory. A more serious objection to this theory was regarding the nature of medium, through which the light travels while coming from sun to earth, since major portion of space in between has vaccum. This hurdle was overcome by processing a hypothetical medium 'ether'. The theory was, later on, modified by Max Planck by saying that the source of light does not give out continuous disturbance. Instead, it emits certain packets of energy consisting of vibratory energy. The modified theory is called Plank's quantum theory and the packet of energy is treated to be the fundamental particle of light known as photon .
7. INTERFERENCE
When two persons try to do the same job, they're said to Interfere with each other's work. They may help or oppose each other. A ray of light (wave motion) imparts some amplitude to the particles of a medium. In the event of two rays travelling through that medium, simultaneously, the particle will be subjected to vibrations from both of them. This displacement of the particle gets modified. The rays are said to have interfered with each other.
Consider a screen being uniformly illuminated by a source 'S1' [Fig.17.15(a)]. Let i be the intensity at any of its points. Let another source 'S2' be placed near it.
If two sources are similar, every point on the screen should have same intensity '2i' [Fig.17.15(b)]. If the two sources satisfy some conditions the intensity of light on screen gets modified. Some portions of the screen have intensity '4i' while some others have no intensity at all.
This modification in the distribution of light energy obtained by the superposition of two or more waves is called Interference .
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