DIFFRACTION

Diffraction is a phenomenon in which a light beam bends around the corner of an obstacle and spreads into the geometric shadow of that obstacle.

FRESNEL AND FRAUNHOFER DIFFRACTION

Diffraction can be classified into two categories:

• 1. Fresnel diffraction

• 2. Fraunhofer diffraction

The distinction between these two categories is as follows:

• a. In Fresnel diffraction, the screen and source are at a finite distance from an obstacle. The distances are important in this class. In Fraunhofer diffraction, the source and screen are at an infinite distance from an obstacle. Therefore, inclination is important.

• b. The incident wavefront in Fresnel diffraction is either spherical or cylindrical, whereas the incident wavefront in Fraunhofer diffraction is planar.

• c. In Fresnel diffraction, the central point of the screen is either bright or dark depending on the number of zones, whereas in Fraunhofer diffraction, the central point of the screen is always bright.

FRAUNHOFER DIFFRACTION DUE TO SINGLE SLIT

Let us consider a monochromatic light source of wavelength ƛ placed at the focus of convex lens L1. The collimated rays of plane wavefront are incident on a single-slit AB of width “e.” The un-deviated rays from the slit reaches at point O, and the rays diffracted by an angle θ reach at P on the screen, as shown in Figure 12.1.

List of Experiments

• 1. Determine the energy band gap of N-type Germanium (Ge) semiconductor using the four-probe method.

• 2. Verify Stefan's fourth power law for black body radiation and determine the exponent of temperature.

• 3. Study of thermoelectricity: Determine thermopower of copper-constantan thermocouple.

• 4. Study the variation of magnetic field with distance along the axis of current-carrying coil and then estimate the radius of the coil.

• 5. Study of Carrey Foster bridge: Determine resistance per unit length of the bridge wire and of a given unknown resistance.

• 6. Determine specific charge (charge to mass ratio; e/m) for electron.

• 7. Study of tangent galvanometer: Determine reduction factor and horizontal component of the earth's magnetic field.

• 8. Determine the wavelength of sodium light using Newton's rings method.

• 9. Determine the concentration of sugar solution using half-shade polarimeter.

• 10. Determine the wavelength of spectral lines of mercury (for violet, green, yellow-1, and yellow-2) using plane transmission grating.

• 11. Determine the charge sensitivity and ballistic constant of a ballistic galvanometer.

• 12. Determine the wavelength of spectral lines of hydrogen and hence the value of Rydberg constant.

• 13. Draw the V-I characteristic of light-emitting diode (LED) and determine the value of Planck's constant.

Experiment 1: Band Gap of Semiconductor

Objective: To determine the energy band gap of n-type Ge-semiconductor using four-probe method.

Apparatus Used: The following apparatus are used in this experiment:

• 1. Probe arrangement (shown in Figure 14.1).

• 2. n-type Ge-crystal chip with nonconducting base.

• 3. Oven with temperature up to 200°C.

• 4. A constant current generator power supply.

• 5. Power source for the oven.

• 6. Thermometer.

NANO

The term “nano” is derived from a Greek word that means “dwarf” (small) and is represented by the symbol “n.” As a unit prefix, it signifies “one billionth,” denoting a factor of 10-9 or 0.000000001. It is primarily used with the metric system, as illustrated in Figures 8.1 and 8.2. For example, one nanometer is equal to 1 × 10-9 m, and one nanosecond is equal to

1 × 10-9 sec. It is frequently encountered in science and electronics, particularly for prefixing units of time and length.

HISTORY OF NANOTECHNOLOGY

The origin of nanotechnology is often attributed to American physicist Richard Feynman's speech, “There's Plenty of Room at the Bottom,” which he gave on December 29, 1959, at an American Physical Society conference at Caltech. A 1959 lecture by Richard Feynman served as the intellectual inspiration for the field of nanotechnology. The term “nanotechnology” was initially used in a conference in 1974 by a Japanese scientist by the name of Norio Taniguchi from Tokyo University of Science to describe semiconductor techniques with characteristic control on the order of a nanometer, such as thin film deposition and ion beam milling. According to his definition, “nanotechnology” is primarily the processing, separation, consolidation, and deformation of materials by a single atom or molecule.

INTRODUCTION

Classical mechanics is mainly based on Newton's laws of motion and gravitation. Initially, it was thought that Newton's second law of motion was valid and applicable at all speeds. But new experimental evidence showed that Newton's second law of motion is valid and applicable at low speeds and invalid when the object is moving at high speeds comparable to the velocity of light. This failure of classical mechanics led to the development of the special theory of relativity by young physicist Albert Einstein in 1905, which showed everything in the universe is relative and nothing is absolute. Relativity connects space and time, matter and energy, electricity and magnetism, which are useful and remarkable to our understanding of the physical universe.

The special theory of relativity is applicable to all branches of modern physics, high-energy physics, optics, quantum mechanics, semiconductor devices, atomic theory, nanotechnology, and many other branches of science and technology.

The theory of relativity has two parts: the special theory of relativity and the general theory of relativity. The special theory of relativity deals with the inertial frame of references, while the general theory of relativity deals with the accelerated frame of references. Some common technical terms that are frequently used in relativistic mechanics are as follows:

• 1. Particle:A particle is a tiny bit of matter with almost no linear dimensions and is considered to be located at a single place. Its mass and charge define it. Examples include the electron, proton, and photon, among others.

Stationary charges give rise to electric fields. Moving charges give rise to magnetic fields. In this chapter, we explore how this comes about, starting with currents in wires which give rise to a magnetic field wrapping the wire.

In this chapter, we rewrite the Maxwell equations yet again, this time in the language of actions and Lagrangians that we introduced in the first book in this series. This provides many new perspectives on electromagnetism. Among the pay-offs are a deeper understanding, via Noether’s theorem, of the energy and momentum carried by electromagnetism fields. This will also allow us to explore a number of deeper ideas, including superconductivity, the Higgs mechanism, and topological insulators.

Take an electric charge and shake it and it will produce light. The purpose of this chapter is to explain how this works.

There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like.

This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.

Newtons laws of motion are not the last word in classical mechanics. In the 250 years after Newton, physicists and mathematicians found ways to reformulate classical mechanics, providing powerful tools to solve problems but, equally as importantly, giving us a new perspective on the laws that govern our universe. This chapter takes the first step in this direction. We will introduce the wonderful principle of least action, a simple rule that underlies all known laws of physics. This will give us new insights, not least the wonderful Noethers theorem, relating symmetries to conservation laws.

The fundamentals of electromagnetism are simple. Moving electric charges set up electric and magnetic fields. In turn, these fields make the charges move. This dance between charges and fields is described by the Maxwell equations. This brief chapter describes how this comes about. It is, in a sense, everything you need to know about electromagnetism, enshrined in these simple equations. The rest of the book is mere commentary.

The laws of classical mechanics are valid in so-called inertial frames. Roughly speaking, these are frames that are at rest. But what if you, one day, find yourself in a frame that is not in- ertial? For example, suppose that every 24 hours you happen to spin around an axis which is 2500 miles away. What would you feel? Or what if every year you spin around an axis 36 million miles away? Would that have any effect on your everyday life? In this chapter, we describe what happens if you sit in a rotating reference frame and the effects of the resulting centrifugal and Coriolis forces.