engineering-physics-sample-notes.pdf

# Engineering Physics Unit - 1 Wave Optics ## Optics Optics is a branch of physics which deals with the "Theory of light and its propagation in a given medium". ### Ray Optics - It deals with image formation by optical systems. ### Wave Optics - It deals with the nature of light. - It is the s...

# Engineering Physics Unit - 1 Wave Optics ## Optics Optics is a branch of physics which deals with the "Theory of light and its propagation in a given medium". ### Ray Optics - It deals with image formation by optical systems. ### Wave Optics - It deals with the nature of light. - It is the study of how light behaves when it propagates as a wave. ## Wave Optics Terms and Concepts **Displacement (m)** - **Amplitude:** Maximum displacement moved by a point on a vibrating body or wave. - **Wavelength:** The distance between two successive crests or troughs of a wave. - **Frequency:** The number of waves that pass a fixed point in a given amount of time. - **Path Difference:** The difference in the path traversed by the two waves. - **Phase Difference:** The difference in the phase angle of two waves. ## Interference of Light Interference is the natural phenomenon in which two waves superimpose to form a resultant wave, which can be of higher or lower amplitude on the same amplitude. ### Examples - It is demonstrated by light reflected from a film of oil floating on water. - Soap Bubble. ## Types of Interference - **Constructive Interference:** when intensity is maximum, interference is called constructive. - **Destructive Interference:** When intensity is minimum, interference is called destructive. ### Constructive Interference - _A = A1 + A2_ ### Destructive Interference - _A = A1 - A2_ ## Condition for Sustained Interference - Should have same frequency, wavelength, amplitude with zero path and phase difference. - Separation between two slits should be very small. - Separation between screen and slits should be large. ## Michelson Interferometer The Michelson interferometer produces interference fringes by splitting a beam of light so that one beam strikes a fixed mirror and the other a movable mirror. When the reflected beams are brought back together an interference pattern results. ### Diagram A diagram of the Michelson Interferometer is depicted. The diagram shows a monochromatic light source, a convex lens, a beam splitter, two plane mirrors (one fixed and one movable), a compensatory plate, and a telescope. ## Fraunhofer's Diffraction at a Single Slit - **Intensity and Position of Central Maxima**: The central maximum of the diffraction pattern is the most intense, and its width is greater than the width of the other maxima. - **Position of Minima**: The minima of the diffraction pattern occur at angles given by the equation _sin theta = m(lambda)/a_, where _m_ is an integer, _lambda_ is the wavelength of the light, and _a_ is the width of the slit. - **Intensity and Position of Secondary Maxima**: The secondary maxima of the diffraction pattern are less intense than the central maximum, and their width is less than the width of the central maximum. - **Width of Principal Maxima**: The width of the principal maxima in a single-slit diffraction pattern is inversely proportional to the width of the slit. ## Wave Nature of Light - Although the wave nature of light falls to explain the phenomena of compton effect, photoelectric effect, continuous X-ray spectrum and blackbody radiation. ## Compton Effect When a beam of monochromatic X-ray is incident on graphite block, it gets scattered. **Variables:** - **p'sin theta = h(nu) sin theta** - p' is the momentum the photon - h is Planck's constant - nu is the frequency of the light - theta is the angle of scattering - **Ep' = h(nu)'** - Ep' is the energy of the scattered photon - h is Planck's constant - nu' is the frequency of the scattered light - **p'cos theta = h(nu) cos theta** - p' is the momentum of the photon - h is Planck's constant - nu is the frequency of the light - theta is the angle of scattering - **Pe´cos theta = mu cos theta** - Pe' is the momentum of the recoiled electron - m is the mass of the electron - u is the velocity of the recoiled electron - theta is the angle of scattering - **Pe´sin theta = musin theta** - Pe' is the momentum of the recoiled electron - m is the mass of the electron - u is the velocity of the recoiled electron - theta is the angle of scattering. - **A photon which is incident on graphite block emits two types of photon wavelength (st' and st')** - **Compton Shift Delta(lambda) = lambda' - lambda , lambda' > lambda** ## Coherence and Optical Fibers Coherence: When two or more light waves reach a point in space with phase difference is about to zero and minimum path difference from source and having same wavelength, frequency and amplitude then these lights wave will be coherent to each other and this nature of light waves is known as Coherence. ### Types of Coherence 1. **Temporal Coherence:** It is a measure of the correlation between the phase of the light wave at different points along the direction of propagation. It is the correlation between the waves at one place at different times along the path of a beam called 'Temporal Coherence'. 2. **Spatial Coherence:** It refers to the consistency of the phase between waves at different points in space, often observed in interference and diffraction patterns. **Coherence Length and Coherence Time** - **The average coherence length of the wave trains for which the field remains sinusoidal is called Coherence Length.** - **It is denoted by Lc.** - **Lc = c * Tc** - Lc is the coherence length - c is the speed of light - Tc is the coherence time - **And the average time interval during which the field remains sinusoidal and the phase of the wave train can be predicted reliably. It is denoted by Tc.** - **Tc = Lc / c** - Tc is the coherence time - Lc is the coherence length - c is the speed of light ## LASER [Light Amplification by Stimulated Emission of Radiation] - Laser is a device that stimulates atoms or molecules to emit light at particular wavelengths and amplifies that light, typically producing a very narrow beam of radiation. - The theoretical basis for the development of laser was provided by Albert Einstein in 1917. ## Laser Terms - **Definitions:** - Production of LASER is a particular consequence of the interaction of radiation with matter. - **Stimulated Absorption:** - Let us consider 3 energy levels in an atom. - The lower energy level is E1 and the higher energy level is E2. - An atom particle initially in E1 can be raised to E2 by absorbing some energy incident on it in the form of light. - The probability of this transition depends on the two energy levels under consideration. It also depends on the number of photons incident on the system. ## Emission **1. Spontaneous Emission** - When an atom is excited to a higher energy level, it has a small life time (10^-8 seconds). - So it can jump from the higher energy level to its ground state by emitting a photon of frequency. - This is called as spontaneous emission. - **P21 = A21** - **R21 = N2A21** - N2 = number of atoms in E2. - R21 = rate of number of atoms going from 2nd energy level to 1st energy level. - **A21:** Einstein's co-efficient of spontaneous emission. **2. Stimulated Emission:** - As per Einstein, when energy incident on a system, it is not essential that it may always be absorbed by the ground state atom. - It can also interact with an atom in an excited state and induce that atom to emit a new photon. - This process of emission is known as or included as stimulated emission. ## Purchase the Notes - Hand-written notes. - Most questions. - All branches. - 100 INR per semester (all subjects), 50 INR per specific subject. - Minimum 100% of the amount will be donated to charity. ## How to Get the Notes 1. **Make payment using UPI ID:** sahilkagyan337@ybl 2. **Take a screenshot of the transaction and send it to this email address:** [email protected] 3. **Access all notes and most questions.** ## QR Code A QR code for phone pe is provided. The user name on the phone pe account is SAHIL KHAN.