B Tech – Physics First year Question paper Solved

B.Tech. DEGREE EXAMINATION
(Examination at the end of First Year)
Paper – III : Physics

Write the characteristics of ultrasonics.

1. High frequency: Ultrasonics refers to sound waves with frequencies higher than 20,000 Hz.
2. Inaudible to human ear: The high frequency of ultrasonic waves makes them inaudible to human ears.
3. Propagation in solids: Ultrasonic waves can propagate through solids, liquids, and gases.
4. Reflection and absorption: Ultrasonic waves can be reflected and absorbed by different materials.
5. Non-destructive testing: Ultrasonics are used for non-destructive testing and evaluation of materials.
6. Medical applications: Ultrasonics have various medical applications, such as imaging and therapy.
7. Industrial uses: Ultrasonics are used in industries for cleaning, welding, and measuring.

Describe phenomenon of double refraction.

Double refraction is a property of certain materials, where a single beam of light is split into two separate beams after passing through the material. This occurs because the material has a different refractive index for light polarized in different directions, causing the light to bend differently as it passes through the material. This results in two separate refracted beams, each with its own direction and angle of refraction. Double refraction is most commonly observed in materials with a crystalline structure, such as calcite, where the refractive index varies depending on the orientation of the crystal lattice.

Write the Faraday‟s laws of electromagnetic induction.

Faraday’s laws of electromagnetic induction are three laws that describe the relationship between a magnetic field and an electric circuit. They are:

1. The first law states that the induced electromotive force (EMF) in a circuit is proportional to the rate of change of magnetic flux through the circuit.
2. The second law states that the direction of the induced EMF is such that it opposes the change in magnetic flux that produced it. This is known as Lenz’s law.
3. The third law states that the induced EMF in a closed loop is equal to the negative of the rate of change of magnetic field in the loop, integrated over time. This is known as Faraday’s law of electromagnetic induction.

These laws form the basis for many applications of electromagnetic induction, including electric generators, transformers, and induction motors.

Explain Heisenberg‟s incertainty principle.

Heisenberg’s uncertainty principle states that it is impossible to simultaneously determine both the position and momentum of a particle with absolute certainty. The more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.

The uncertainty principle can be mathematically expressed as an inequality, where the product of the uncertainties in position and momentum is equal to or greater than a constant, called the Planck constant divided by 2π. This means that the product of the uncertainties in position and momentum can never be smaller than this constant, so that it is impossible to measure both quantities with perfect accuracy at the same time.

The uncertainty principle has important implications for the behavior of subatomic particles, and it is a fundamental principle of quantum mechanics. It limits the ability of physicists to precisely measure the properties of particles and has far-reaching implications in fields such as quantum cryptography, quantum computing, and quantum field theory.

Write about spontaneous emission and stimulated emission.

Spontaneous emission and stimulated emission are two distinct processes of light emission in atoms and molecules.

Spontaneous emission is the emission of light or photons from an excited state of an atom or molecule without any external influence. It is a random process and occurs spontaneously due to the transition of an electron from a higher energy state to a lower energy state. The light emitted during spontaneous emission has no specific direction or phase.

Stimulated emission, on the other hand, is the emission of light or photons from an excited state of an atom or molecule in response to the presence of a photon of the same frequency. When a photon of the correct frequency passes through an excited atom or molecule, it stimulates the emission of a photon with the same frequency, phase, and direction as the incoming photon. This results in the amplification of light and is the principle behind laser (Light Amplification by Stimulated Emission of Radiation) technology.

In summary, spontaneous emission is a random process, while stimulated emission is triggered by the presence of light, leading to the amplification of light.

Describe Kerr and Faraday effects.

Kerr and Faraday effects are two distinct optical effects that describe the interaction of light with matter.

The Kerr effect, also known as the electro-optic effect, is the change in the refractive index of a material as a result of an electric field applied to it. When an electric field is applied to a medium, it causes the polarization of the medium, leading to a change in its refractive index. The magnitude of the Kerr effect is proportional to the strength of the electric field, and it is a non-linear optical effect. This effect is used in optical switching, modulators, and other optical devices.

The Faraday effect, also known as the magneto-optic effect, is the rotation of the plane of polarization of light as it passes through a magnetic field. When light passes through a magnetic field, the electrons in the medium are affected by the magnetic field, leading to a change in the refractive index. This change in the refractive index results in a rotation of the plane of polarization of the light, which is proportional to the strength of the magnetic field and the length of the path traveled by the light. The Faraday effect is used in magnetic field sensors, magneto-optic data storage, and other applications.

In summary, the Kerr effect is the change in refractive index due to an electric field, while the Faraday effect is the rotation of the plane of polarization due to a magnetic field.

Explain the principle and working of Michelson interferometer and write about antireflection coatings

A Michelson interferometer is a type of optical interferometer that uses the interference of light to measure the difference in path length between two separate beams of light. The basic principle behind the Michelson interferometer is the superposition of two coherent light beams, which results in the creation of an interference pattern.

The Michelson interferometer consists of a beamsplitter, two mirrors, and a detector. Light from a laser source is split into two separate beams by the beamsplitter, one of which is directed towards a stationary mirror and the other towards a movable mirror. The two beams are then recombined by the beamsplitter and the resulting interference pattern is detected by a photodetector.

The difference in path length between the two beams can be controlled by adjusting the position of the movable mirror. By analyzing the interference pattern, the difference in path length can be determined with high precision. The Michelson interferometer is widely used in fields such as metrology, interferometry, and testing of optical components.

Antireflection coatings are thin optical coatings applied to surfaces to reduce the amount of light reflected by the surface. The coatings work by creating an optical interference that reduces the reflectance of the surface, improving the transmission of light through the surface. Antireflection coatings are used in a variety of applications, including optical components, lenses, and solar cells. The coatings can be made from materials such as metals, dielectrics, or multi-layer stacks of different materials, and their properties can be tailored for specific wavelength ranges and applications.

Describe Magnetostriction and piezo-electric oscillator methods in production of
ultrasonic waves.

Magnetostriction and piezoelectric oscillator methods are two common techniques used in the production of ultrasonic waves.

Magnetostriction is the phenomenon in which the dimensions of a ferromagnetic material change as a result of an applied magnetic field. In the production of ultrasonic waves using the magnetostriction method, a ferromagnetic material is magnetized and de-magnetized at a high frequency, leading to cyclic changes in the dimensions of the material. This creates ultrasonic waves that propagate through the material. The magnetostriction method is commonly used in the production of low-frequency ultrasonic waves.

The piezoelectric oscillator method uses the piezoelectric effect, in which a material generates a voltage as a result of mechanical stress or strain. In the production of ultrasonic waves using the piezoelectric oscillator method, a piezoelectric material is subjected to an alternating voltage, leading to cyclic changes in its dimensions. This creates ultrasonic waves that propagate through the material. The piezoelectric oscillator method is commonly used in the production of high-frequency ultrasonic waves.

In summary, the magnetostriction method uses the change in dimensions of a ferromagnetic material due to an applied magnetic field to produce ultrasonic waves, while the piezoelectric oscillator method uses the piezoelectric effect to generate ultrasonic waves through cyclic changes in the dimensions of a piezoelectric material.

Obtain an expression for electric potential due to point charge and charged disc.

Electric potential due to a point charge: V = k * Q / r

where V = electric potential, k = Coulomb’s constant, Q = charge of the point charge, and r = distance from the point charge.

Electric potential due to a charged disc: V = k * Q / (2 * h) * ln(R / r)

where V = electric potential, k = Coulomb’s constant, Q = charge of the disc, R = radius of the disc, r = distance from the center of the disc, and h = perpendicular distance from the point to the plane of the disc.

Write the Manwell‟s equations. Obtian an expression for resonance frequency in a
LCR series circuit.

Manwell’s Equations: Manwell’s equations are used to describe the behavior of a simple electrical circuit that contains an inductor (L), a capacitor (C), and a resistor (R).

i = I_m * sin(wt + Φ) V_L = L * di/dt = L * w * I_m * cos(wt + Φ) V_C = 1/C * ∫i dt = 1/C * I_m * sin(wt + Φ) V_R = R * i = R * I_m * sin(wt + Φ)

where i is the current in the circuit, I_m is the maximum current, w is the angular frequency, t is time, Φ is the phase angle, V_L is the voltage across the inductor, V_C is the voltage across the capacitor, and V_R is the voltage across the resistor.

Expression for Resonance Frequency in a LCR Series Circuit: The resonance frequency in a series LCR circuit is defined as the frequency at which the circuit’s impedance is at a minimum.

f_r = 1 / (2 * pi * √(L * C))

where f_r is the resonance frequency, L is the inductance, C is the capacitance, and pi is the mathematical constant π.

Write about G.M. Counter and scintillation counter

G.M. Counter: G.M. Counter, also known as Geiger-Müller counter, is a type of particle detector that is commonly used to detect ionizing radiation such as alpha particles, beta particles, and gamma rays. It works on the principle of ionization of gas by radiation. When ionizing radiation enters the chamber, it ionizes the gas molecules, creating ions and electrons. The high voltage applied across the electrodes in the chamber accelerates the ions and electrons towards the electrodes, producing a pulse of current that is proportional to the energy of the incident radiation. This pulse of current is then amplified and counted, providing a measure of the amount of ionizing radiation present.

Scintillation Counter: Scintillation counter is a type of particle detector that is commonly used to detect ionizing radiation. It works on the principle of scintillation, which is the process of light emission that occurs when high-energy particles pass through certain materials such as scintillation crystals. When ionizing radiation enters the scintillation crystal, it excites the atoms, causing them to emit light. The light is then detected by photomultiplier tubes, which convert the light into electrical signals. These electrical signals are then amplified and counted, providing a measure of the amount of ionizing radiation present.

Compared to G.M. Counters, scintillation counters have higher energy resolution and are capable of detecting lower-energy ionizing radiation. However, they are generally more complex and expensive than G.M. Counters. Both types of counters are widely used in various applications such as radiation therapy, nuclear medicine, and nuclear physics research.

Distinguish between MB, BE and Fp statistics. Obtain expression for distribution
function in FD statisties.

MB, BE, and Fp Statistics: MB, BE, and Fp statistics are used to describe the performance of a binary classifier, which is a type of machine learning algorithm that classifies data into two categories (e.g. positive/negative, true/false).

MB (Misclassification Rate) is the ratio of the number of incorrect predictions made by the classifier to the total number of predictions. BE (Brier Score) measures the mean squared error between the predicted probabilities and the true class labels. Fp (False Positive Rate) is the ratio of the number of incorrect positive predictions to the total number of positive predictions.

Expression for Distribution Function in FD Statistics: The distribution function in FD (False Discovery Rate) statistics is used to describe the probability that a null hypothesis is incorrectly rejected as true (i.e. a false discovery).

FD = (V / R)

where FD is the false discovery rate, V is the number of false discoveries, and R is the number of rejected null hypotheses. The distribution function can be used to control the false discovery rate, ensuring that the rate of false discoveries is kept at a desired level. This is useful in applications such as multiple hypothesis testing, where multiple tests are performed on a large number of hypotheses, and it is important to control the number of false discoveries.

Write the construction and working of Ruby laser and He-Ne gas laser.

Ruby Laser:

Construction: The Ruby laser consists of a cylindrical ruby crystal (typically 6 mm in diameter and 30 mm long), two mirrors, a flashlamp, and a power supply. The ruby crystal is placed between the two mirrors, one of which is partially reflective and allows some of the light to pass through while reflecting the rest back into the crystal. The flashlamp is placed around the ruby crystal and is used to pump energy into the crystal, exciting the atoms and causing them to emit light.

Working: The Ruby laser operates in a pulsed mode. The flashlamp is energized, causing a burst of light to enter the ruby crystal. The light is absorbed by the chromium ions in the crystal, exciting them to a higher energy state. As the chromium ions relax back to their ground state, they emit light at a specific wavelength (694.3 nm). This light is amplified as it passes through the ruby crystal, reflecting back and forth between the two mirrors and building up in intensity. Some of the light eventually escapes the crystal through the partially reflective mirror, producing the laser output.

He-Ne Gas Laser:

Construction: The He-Ne gas laser consists of a cylindrical tube filled with a mixture of helium and neon gases, two mirrors, and a power supply. One of the mirrors is partially reflective, allowing some of the light to escape the tube while reflecting the rest back into the gas mixture. The tube is placed between the two mirrors, and the power supply is used to create an electrical discharge through the gas mixture.

Working: The He-Ne gas laser operates in a continuous mode. The electrical discharge excites the helium and neon atoms in the gas mixture, causing them to emit light. This light is amplified as it passes through the gas mixture, reflecting back and forth between the two mirrors and building up in intensity. Some of the light eventually escapes the tube through the partially reflective mirror, producing the laser output. The He-Ne laser emits light at a specific wavelength (632.8 nm), which is determined by the composition of the gas mixture.

Both the Ruby laser and the He-Ne gas laser are commonly used in a wide range of applications, including industrial and scientific applications, medical and surgical applications, and entertainment and lighting applications.

Describe Messner effect. Write the applications of High temperature superconduction

Messner Effect: The Messner Effect is a phenomenon that occurs in superconductors when the magnetic field created by the flow of electrical current exceeds a critical value, causing the superconductivity to be lost. This effect is named after the physicist J. Messner, who first observed it in superconducting thin films.

The Messner effect is a result of the interaction between the magnetic field and the superconducting electrons. When the magnetic field exceeds the critical value, it can cause the superconducting electrons to pair up and form what is known as a vortex, which in turn destroys the superconductivity.

Applications of High Temperature Superconductors:

High temperature superconductors (HTS) are materials that exhibit superconducting properties at relatively high temperatures, typically above the boiling point of nitrogen (77 K). The discovery of HTS has opened up new possibilities for a wide range of applications, including:

1. Magnetic Resonance Imaging (MRI) – HTS can be used in MRI machines to create strong magnetic fields, which are used to image the body’s internal organs and tissues.
2. Power Generation and Transmission – HTS can be used to improve the efficiency and reduce the losses in power generation and transmission.
3. Energy Storage – HTS can be used to store energy in the form of magnetic energy, making it possible to store energy more efficiently and at a lower cost.
4. Particle Accelerators – HTS can be used in particle accelerators to create strong magnetic fields, which are used to accelerate particles to high speeds.
5. Levitation Applications – HTS can be used in levitation applications, such as high-speed trains, where the trains can be levitated above the tracks, reducing friction and increasing efficiency.
6. Sensors and Detectors – HTS can be used in a variety of sensors and detectors, including magnetic sensors, Hall effect sensors, and Josephson junction devices.