Lecture 3-4 Fluid Flow & Viscosity PDF

Lecture 3 LEARNING OBJECTIVE EXPLAIN THE FLUID FLOW EXPLAIN THE APPLICATION OF CONTINUITY EQUATION IN OUR LIFE EXPLAINE BERNOULLI’S EQUATION AND ITS APPLICATION Fluid flow Fluid flow can be characterized as steady or unsteady. When the flow is steady, the velocity of the...

Lecture 3 LEARNING OBJECTIVE EXPLAIN THE FLUID FLOW EXPLAIN THE APPLICATION OF CONTINUITY EQUATION IN OUR LIFE EXPLAINE BERNOULLI’S EQUATION AND ITS APPLICATION Fluid flow Fluid flow can be characterized as steady or unsteady. When the flow is steady, the velocity of the fluid at any point is constant in time. Steady flow is laminar. The fluid flows in neat layers so that each small portion of fluid that passes a particular point follows the same path as every other portion of fluid that passes the same point. The path that the fluid follows, starting from any point, is called a streamline When the fluid velocity at a given point changes, the flow is unsteady. Turbulence is an example of unsteady flow. The flow velocity at any point changes erratically; prediction of the direction or speed of fluid flow under turbulent conditions is difficult. Laminar and Turbulent Flow Ideal fluid flow An ideal fluid is incompressible, undergoes laminar flow, and has no viscosity. The flow of an ideal fluid is described by two principles: the continuity equation and Bernoulli’s equation. The continuity equation is an expression of conservation of mass for an incompressible fluid: since no fluid is created or destroyed, the total mass of the fluid must be constant. Bernoulli’s equation is a form of the energy conservation law applied to fluid flow. These two equations enable us to predict the flow of an ideal fluid.  Suppose an incompressible fluid flows into a pipe of nonuniform cross-sectional area under conditions of steady flow. The fluid on the left moves at speed v1. During a time Δt, the fluid travels a distance The Continuity Equation The same volume of fluid that enters the pipe in a given time interval exits the pipe in the same time interval. Where the radius of the tube is large, the speed of the fluid is small; where the radius is small, the fluid speed is large. EXAMPLE The heart pumps blood into the aorta, which has an inner radius of 1.0 cm. The aorta feeds 32 major arteries. If blood in the aorta travels at a speed of 28 cm/s, at approximately what average speed does it travel in the arteries? Assume that blood can be treated as an ideal fluid and that the arteries each have an inner radius of 0.21 cm. Bernoulli’s equation According to the continuity equation, the fluid must speed up as it enters a constriction and then slow down to its original speed when it leaves the constriction. The pressure of the fluid in the constriction (P2) cannot be the same as the pressure before or after the constriction (P1). For a horizontal flow, the speed is higher where the pressure is lower. This principle is often called the Bernoulli effect. EXAMPLE A Venturi meter measures fluid speed in a pipe. A constriction (of cross-sectional area A2) is put in a pipe of normal cross-sectional area A1. Two vertical tubes, open to the atmosphere, rise from two points, one of which is in the constriction. The vertical tubes function like manometers, enabling the pressure to be determined. From this information the flow speed in the pipe can be determined. EXAMPLE Suppose that the pipe in question carries water, A1= 2.0A2, an d the fluid heights in the vertical tubes are h1 = 1.20 m and h2 = 0.80 m. (a) Find the ratio of the flow speeds v2/v1. (b) Find the gauge pressures P1 and P2. (c) Find the flow speed v1 in the pipe. Application of Bernoulli’s Principle: Arterial Flutter and Aneurisms Suppose an artery is narrowed due to buildup of plaque on its inner walls. The flow of blood through the constriction will have high velocity. Bernoulli’s equation tells us that the pressure P2 in the constriction is lower than the pressure elsewhere. The arterial walls are elastic rather than rigid, so the lower pressure allows the arterial walls to contract a bit in the constriction. Now the flow velocity is even higher and the pressure even lower. Eventually the artery wall collapses, shutting off the flow of blood. Then the pressure builds up, reopens the artery, and allows blood to flow. The cycle of arterial flutter then begins again. The opposite may happen where the arterial wall is weak. Blood pressure pushes the artery walls outward, forming a bulge called an aneurism. The lower flow speed in the bulge is accompanied by a higher blood pressure, which enlarges the aneurism even more. Ultimately the artery may burst from the increased pressure.  Lecture 4 LEARNING OBJECTIVE EXPLAIN WHAT IS THE VISCOSITY AND IT’S APPLICATION IN MEDICINE APPLY POISEULLE’S LAW FOR VISCUS FLOW  Viscosity is the resistance of a fluid (liquid or gas) to a change in shape, or movement of Viscosity neighbouring portions relative to one another. Viscosity denotes opposition to flow.  VISCOSITY Bernoulli’s equation ignores viscosity (fluid friction). However, all real fluids have some viscosity; to maintain flow in a viscous fluid, we have to apply an external force since viscous forces oppose the flow of the fluid. A pressure difference between the ends of the pipe must be maintained to keep a real liquid moving through a horizontal pipe. A liquid is more viscous if the cohesive forces between molecules are stronger. The viscosity of a liquid decreases with increasing temperature because the molecules become less tightly bound. Gases, on the other hand, have an increase in viscosity for an increase in temperature. At higher temperatures the gas molecules move faster and collide more often with each other. VISCOSITY Viscous flow If there were no viscosity, all the layers would move at the same speed. In viscous flow, the fluid speed depends on the distance from the tube walls. The fastest flow is at the center of the tube. Layers closer to the wall of the tube move more slowly. The outermost layer of fluid, which is in contact with the tube, does not move. The coefficient of viscosity (or simply the viscosity) of a fluid is written as the Greek letter eta (η) and has units of pascal-seconds (Pa⋅s) in SI Poiseuille’s Law (for Viscous Flow) The coefficient of viscosity (or simply the viscosity ) of a fluid is written as the Greek letter eta ( η ) and has units of pascal-seconds (Pa⋅s) in SI. where ΔV /Δt is the volume flow rate, ΔP is the pressure difference between the ends of the pipe, r and L are the inner radius and length of the pipe, respectively, and η is the viscosity of the fluid. EXAMPLE A cardiologist reports to her patient that the radius of the left anterior descending artery of the heart has narrowed by 10.0%. What percent increase in the blood pressure drop across the artery is required to maintain the normal blood flow through this artery?  Chapter 18 Electric Current and Circuits LEARNING OBJECTIVE LECTURE 1 Define the electric current and the emf Explain ohm’s law and the resistance Explain the parameters to change the resistivity S how the diffe re nce be twe e n s e rie s and p arallel circuits LECTURE 2 Explain the analogy between the electrical resistance and resistance of blood vessels E xp lain the factor s that change the blood ve s s e ls resistance Compar e be twe e n p arallel and s e rie s circuits and systemic circulation Slide 1  Lecture 1 Learning objective Define the electric current and the emf Explain ohm’s law and the resistance Explain the parameters to change the resistivity S how how the r e s is tance and r e s is tivity differ for different materials S how the diffe r e nce be twe e n s e rie s and p arallel circuits Slide 2 ELECTRIC CURRENT A net flow of charge is called an electric current. The current (symbol I) is defined as the net amount of charge passing per unit time through an area perpendicular to the flow direction. Δq is the net charge that passes through the surface during a time interval Δt. The SI unit of current, equal to one coulomb per second, is the ampere (A) 1 C = 1 A.s  EXAMPLE Two wires of cross-sectional area 1.6 mm2 connect the terminals of a battery to the circuitry in a clock. During a time interval of 0.040 s, 5.0 ×1014 electrons move to the right through a crosssection of one of the wires. What is the magnitudeof the current in the wire? Solution EMF AND CIRCUITS To maintain a current in a conducting wire, we need to maintain a potential difference between the ends of the wire. One way to do that is to connect the ends of the wire to the terminals of a battery (one end to each of the two terminals). The potential difference maintained by an ideal battery is called the battery’s emf (symbol ℰ). emf is measured in units of potential (volts) and is a measure of the work done by the battery per unit charge. RESISTANCE AND RESISTIVITY Suppose we maintain a potential difference across the ends of a conductor. How does the current ‘I’ that flows through the conductor depend on the potential difference ‘ΔV’ across the conductor? For many conductors, the I is proportional to ΔV. This relationship is known as Ohm’s law I ∝ ΔV I=R ΔV The electrical resistance R is defined to be the ratio of the potential difference (or voltage) ΔV across a conductor to the current I through the material. Δ𝑉 𝑅= 𝐼 In SI units, electrical resistance is measured in ohms (symbol Ω, the Greek capital omega), defined as 1 Ω = 1 V/A Resistivity Resistance depends on size and shape. We expect a long wire to have higher resistance than a short one (everything else being the same) and a thicker wire to have a lower resistance than a thin one. The electrical resistance of a conductor of length ‘L’and cross-sectional area ‘A’ can be written: 𝐿 𝑅=𝜌 𝐴 The constant of proportionality ρ (Greek letter rho), which is an intrinsic characteristic of a particular material at a particular temperature, is called the resistivity of the material. The SI unit for resistivity is Ω·m. The inverse of resistivity is called conductivity [SI units (Ω·m)−1]. RESISTANCE AND RESISTIVITY Slide 8  EXAMPLE (a) A 30.0-m-long extension cord is made from two copper wires. (The wires carry currents of equal magnitude in opposite directions.) What is the resistance of each wire at 20.0°C? The diameter of wire is 0.912 mm. Slide 9 Resistors A resistor is a circuit element designed to have a known resistance. Resistors are found in virtually all electronic devices. Current in a resistor flows in the direction of the electric field, which points from higher to lower potential. Therefore, if you move across a resistor in the direction of current flow, the voltage drops by an amount IR. As water flows downhill (toward lower potential energy); electric current in a resistor flows toward lower potential.  SERIES AND PARALLEL CIRCUITS Resistors in Series When one or more electric devices are wired so that the same current flows through each one, the devices are said to be wired in series Slide 15  SERIES AND PARALLEL CIRCUITS ResistorsinSeries Thecircuit showstwo resistorsin series.Thestraight linesrepresent wires,which we assume to have negligible resistance. The same current flows through the emf and the two resistors.  SERIES AND PARALLEL CIRCUITS ResistorsinSeries For any number N of resistors connected in series, Note that the equivalent resistance for two or more resistors in series is larger than any of the resistances.  SERIES AND PARALLEL CIRCUITS Resistors in Parallel When one or more electrical devices are wired so that the potential difference across them is the same, the devices are said to be wired in parallel Slide 14  SERIES AND PARALLEL CIRCUITS ResistorsinParallel In the figure,an emf is connected to three resistors in parallel with each other.Theleft side of each resistor is at the same potential since theyare all connected by wiresof negligible resistance. Likewise,the right sideof each resistor is at the samepotential. Thus,there is a common potential difference across the three resistors. Slide 15  SERIES AND PARALLEL CIRCUITS Resistors in Parallel Applyingthe junction rule to point A yields How much of the current I from the emf flowsthrough each resistor? The Current dividessuch that the potential difference VA −VB must be the same along each of the three paths—and it must equal the emf ℰ. From the definition of resistance, Slide 16  SERIES AND PARALLEL CIRCUITS Resistors in Parallel Therefore, the currents are Slide 17  SERIES AND PARALLEL CIRCUITS ResistorsinParallel The three parallel resistors can be replaced by a single equivalent resistor Req. In order for the same current to flow, Req must be chosen so that ℰ=IReq.ThenI/ℰ=1/Req and Slide 18 For N resistorsconnected in parallel, Note that the equivalent resistance for two or more resistors in parallel is smaller than any of the resistances (1/ Req >1/ Ri ,so Req 30 cm) X-rays and Gamma Rays X-rays have wavelengths ranging from 0.01 to 10 nm, frequency ranging from 30 petahertz to 30 exahertz (3x1016 Hz to 3x1019 Hz). Gamma rays are high energy EM radiation (< 0.01 nm). Pulsars, neutron stars, black holes, and explosions of supernovae are sources of gamma rays that travel toward Earth, but—fortunately for us—gamma rays are absorbed by the atmosphere. Very common application of x-ray in medicine are X-ray imaging and CT scan. Most diagnostic x-rays used in medicine and dentistry have wavelengths between 10 and 60 pm (1 pm = 10−12 m). In a conventional x-ray, film records the amount of x-ray radiation that passes through the tissue. Computed tomography (CT) allows a cross-sectional image of the body.  X-rays X-ray CT scan X-ray CT scan of chest shows lungs, heart and tumour (red)  X-rays Radiotherapy X-rays or other radiation can damage the DNA in cells and kill them. This is why radiation can be dangerous. But cells which are dividing rapidly are more likely to be killed. So, we use x-rays to kill the rapidly- dividing cancer cells. We must still ensure that healthy tissue is undamaged. A linear accelerator generates x-rays. It rotates around the body, irradiating the tumour from all directions A medical physicist decides which angles to shine x-rays from to destroy tumour and minimise damage to other tissue Ultraviolet Ultraviolet (UV) radiation is higher in frequency than visible light. UV ranges in wavelength from the shortest visible wavelength (about 400 nm) down to about 10 nm. There is plenty of UV in the Sun’s radiation. UV incident on human skin causes the production of vitamin D. More UV exposure causes tanning; too much exposure can cause sunburn and skin cancer. UV incident on the eye can cause cataracts. In medicine, ultraviolet radiation is used to treat certain skin conditions such as psoriasis, vitiligo, and skin tumours of cutaneous T-cell lymphoma. Visible light Visible light is the part of the spectrum that can be detected by the human eye. For an average range we take frequencies of 430 THz (1 THz = 1012 Hz) to 750 THz, corresponding to wavelengths in vacuum of 700–400 nm. White light can be separated by a prism into the colours red (700–620 nm), orange (620–600 nm), yellow (600–580 nm), green (580–490 nm), blue (490–450 nm), and violet (450–400 nm). Red has the lowest frequency (longest wavelength), and violet has the highest frequency (shortest wavelength). Lightbulbs, fire, the Sun, and fireflies are some sources of visible light. Most of the things we see are not sources of light; we see them by the light they reflect. Colorimeter and spectrophotometers are working in visible region.  Visible light Medical applications Blue light treatment of jaundice in babies  Visible light Scanning laser ophthalmoscope A scanning laser ophthalmoscope is an instrument that uses a collimated beam of laser light to image the ocular structures of the eye, especially the retina and optic nerve head.  Visible light Photodynamic therapy Photodynamic therapy (PDT) uses a combination of light energy and photosensitizing medications to treat certain types of cancer and other health conditions such as psoriasis, acne and infections.  Visible light An endoscopy is a test to look inside the body. A long, thin tube with Endoscopy a small camera inside, called an endoscope, is passed into body through a natural opening such as mouth.  Visible light New approaches to Endoscopy Infrared Infrared radiation (IR) is lower in frequency than visible light. IR extends from the low-frequency (red) edge of the visible to a frequency of about 300 GHz (λ = 1 mm), ie., 700nm – 1 mm. Infrared waves are longer than visible light waves but shorter than radio waves. Infrared light is invisible to the human eye, but some animals can detect IR. The thermal radiation given off by objects near room temperature is primarily infrared, with the peak of the radiated IR at a wavelength of about 0.01 mm = 10 μm. IR is using in modern thermometers and Thermography.  Infrared Medical application Thermography Thermography is the use of infrared (IR) imaging to assess skin temperature as an extension of the clinician's physical exam to aid in the formation of a medical diagnosis or treatment plan.  Infrared Pulse oximetry Pulse oximetry uses spectrophotometry to determine the proportion of hemoglobin that is saturated with oxygen  Infrared Near Infrared Spectroscopy Near infrared spectroscopy (NIRS) is a tool for assessing of the oxygenation status and hemodynamics of various organs, e.g. muscle and brain. © Christian Klant Photography Microwaves Microwaves are the part of the EM spectrum lying between radio waves and IR, with vacuum wavelengths roughly from 1 mm to 30 cm. Microwaves are used in communications (cell phones, wireless computer networks, and satellite TV) and in radar. Microwave thermotherapy is being used in medicine for cancer treatment and treatment of other diseases. Radio Waves The lowest frequencies (up to about 1 GHz) and longest wavelengths (down to about 0.3 m) are called radio waves. Radio waves extensively used for communications. The three main Radio wave applications in medicine are: MRI – diagnostic imaging RF ablation – cardiology and cancer (tumour) therapy Localized dielectric heating (shortwave diathermy) – physiotherapy. Magnetic Resonance Imaging (MRI) LECTURE 2 Explain what is the MRI and how it is work Explain the safety of using MRI Explain the people who are not able to use MRI Magnetic resonance imaging (MRI) Magnetic resonance imaging (MRI) is an imaging technique used primarily in medical settings to produce high quality images of the inside of the human body. MRI is based on the principles of nuclear magnetic resonance (NMR), a spectroscopic technique used by scientists to obtain microscopic chemical and physical information about molecules. The technique was called magnetic resonance imaging rather than nuclear magnetic resonance imaging (NMRI) because of the negative connotations associated with the word nuclear in the late 1970's. History Felix Bloch and Edward Purcell, both of whom were awarded the Nobel Prize in 1952, discovered the magnetic resonance phenomenon independently in 1946. 1952 2003 In 2003, Paul C. Lauterbur of the University of Illinois and Sir Peter Mansfield of the University of Nottingham were awarded the Nobel Prize in Medicine for their discoveries concerning magnetic resonance imaging. Definition MRI (Magnetic resonance imaging) is an imaging modality based on an interaction between transmitted radiofrequency (RF) waves and hydrogen nuclei in human body under the influence of a strong magnetic field. MRI produces very clear, detailed pictures of the organs and structures in the body Common Uses Physicians use the MRI examination to help diagnose or monitor treatment for conditions such as: Tumors and other cancer related abnormalities. Certain types of heart problems. Blockages or enlargements of blood vessels Diseases of the liver, such as cirrhosis, and that of other abdominal organs. Diseases of the small intestine, colon, and rectum Principles of MRI MRI is based on the measurement of energy emitted from hydrogen nuclei following their simulation by radio frequency signals. The energy emitted varies according to the tissues from which the signals emanate. This allow MRI to distinguish between different tissues.  Theory Our body is made up of living cells… Which are made up of molecules … Which are made up of atoms The simplest atom is… Hydrogen 1 electron 1 proton It’s nucleus contains just one proton How do protons help in MRI Protons are positively charged and have rotatory movement called Spin. Any moving charge generates current. Every current has a small magnetic field around it. So, every spinning proton has a small magnetic field around it. N With out magnetic field S With magnetic field Why proton (H+) only? Other atoms can also be utilized for MRI. The requirement are that their nuclei should have spin and should have odd number of proton within them. Hence theoretically 13C, 19F, 23Na, 31P can be used for MR imaging. Hydrogen atom has only one proton. Hence H+ ion is equivalent to a proton. Hydrogen ions are present in abundance in body water. H+ gives best and most intense signal among all nuclei. MRI working principle This tiny pulse of radio waves that can be detected and analysed. The timing, and the energy of these signals, reveals information about the Hydrogen atoms and what types of molecules they are attached to. Elements of MRI Components of an MRI Machine Magnet Primary component, generates a strong magnetic field. It measured by Tesla (T). Clinical MRI is 1.5-3 T. (Earth magnetic field is 0.00003 T) To create such a large magnetic field, electromagnets are need to be used. Electric current passing through massive coil produce very high temperature. To avoid this, now, MRIs are using Superconducting magnet. Super conducting material work only at extreme low temperature. To cool, liquid helium is using (boiling point of He is -269oC) Components of an MRI Machine Gradient Coils Three gradient coils, one for each of the orthogonal plane, are located within the core of the MRI unit. It alter primary magnet. It used to fine tune the magnetic field so particular body parts and tissue types can be focused on. It is responsible for loud noises in MRI. RF Coil Sends radiofrequency pulses to excite hydrogen atoms. Detects returning signals from the body. Computer System Processes signals and converts them into images. Steps to get MR images 1. Placing the patient in the magnet 2. Sending radiofrequency (RF) pulse by coil 3. The radio wave is turned off 4. Patients body emits a signal 5. Receiving signals from the patient by coil 6. Transformation of signals into image by complex processing in the computers. View an MRI scan from any angle.. https://www.youtube.com/watch?v=NlYXqRG7lus Types of MRI 1. Structural MRI: T1-weighted, T2-weighted, and FLAIR images. 2. Functional MRI (fMRI): Measures brain activity by detecting changes in blood flow. 3. Magnetic Resonance Angiography (MRA): Focuses on blood vessels. 4. Diffusion MRI: Shows movement of water molecules, useful for brain studies. 5. Cardiac MRI: Provides detailed images of the heart. Safety of using MRI Since the magnet used is incredibly strong… Stand 1m away with a large spanner in your hand…. you would not be able to hold on to it. Patients have to remove all metallic objects and credit cards… Patients may have metal objects inside their bodies may not be able to take MRI  Potential Projectiles - examples Cell phone Keys Glasses Hair pins / barrettes Jewelry Safety pins Paper clips Coins Pens Pocket knife Nail clippers Steel-toed boots / shoes Tools Clipboards No loose metallic objects should be taken into the Scan room!  Potential Projectiles – Large Objects Due to the strength of the magnet, large objects such as chairs and IV poles can become projectiles and get stuck in the magnet! Photo credit: www.simplyphysics.com Patients may be asked such as.. Have you ever worked in the army or metal working industry? Metal fragments (especially in the eye) could become dislodged Do you have a pacemaker? If yes you cannot have an MRI scan Do you have any dental implants Some could become magnetised Do you have any metal pins or staples in your body? Some could become magnetised and need to be checked that they will hold in place during the scan People Who Cannot Use MRI Absolute Contraindications: Patients with pacemakers, cochlear implants, or other metallic implants. Relative Contraindications: Pregnancy, tattoos containing metallic ink, claustrophobia (fear of closed spaces), obesity (may need open MRI). People Who Cannot Use MRI Absolute Contraindications: Patients with pacemakers, cochlear implants, or other metallic implants. Relative Contraindications: Pregnancy, tattoos containing metallic ink, claustrophobia (fear of closed spaces), obesity (may need open MRI).  Optics Chapter 23 Chapter 24  Learning Objectives Lecture 1 Explain the refraction of light Explain how can total internal reflection occurs Define the critical angle Explain the medical uses of optical fibers Lecture 2 Describe the types of thin lenses Explain how to find the nature of image for thin  Lecture 1 Explain the refraction of light Explain how can total internal reflection occurs Loading… Define the critical angle Explain the medical uses of optical fibers The refraction of light: Snell’s law Refraction is the change in the direction of a wave passing from one medium to another. Refraction makes it possible for us to have optical instruments such as magnifying glasses, lenses and prisms. n The refractive index, also called the index of refraction, describes how fast light travels i nt through the material. It depends on the material of the medium and the wavelength that passes though. Refractive index (n) Refractive index (n)is defined as the ratio of velocity of light in vacuum to the velocity of light in a substance at same wavelength. In general, light slows somewhat when traveling through a medium. Loading… Dispersion in a Prism When natural white light enters a triangular prism, the light emerging from the far side of the prism is separated into a continuous spectrum of colors from red to violet The separation occurs because the prism is dispersive—that is, the speed of light in the prism depends on the frequency of the light At the front surface of the prism, each light ray of a particular frequency refracts at an angle determined by the index of refraction of the prism at that frequency. The index of refraction increases with increasing frequency, so it is smallest for red and increases gradually until it is largest for violet. As a result, violet bends the most and red the least. Refraction occurs again as light leaves the prism. The geometry of the prism is such that the different colors are spread apart farther at the back surface. Total internal reflection Critical angle: Is the angle of incidence when the angle of refraction is 90°. When light is moving from a denser medium towards a less dense of the light is reflected. This phenomenon is called total internal reflection Total internal reflection (TIR) occurs when: The angle of incidence is greater than the critical angle and the incident material is denser than the second material. Therefore, the two conditions for total internal reflection are: The angle of incidence > the critical angle The incident material is denser than the second material Fiber Optics Total internal reflection is the principle behind fiber optics, a technology that has revolutionized both communications and medicine. At the center of an optical fiber is a transparent cylindrical core made of glass or plastic with a relatively high index of refraction. The core may be as thin as a few micrometers in diameter— quite a bit thinner than a human hair. Surrounding the core is a coating called the cladding, which is also transparent but has a lower index of refraction than the core. Endoscopy In medicine, bundles of optical fibers are at the heart of the endoscope, which is fed through the nose, mouth, or rectum, or through a small incision, into the body. One bundle of fibers carries light into a body cavity or an organ and illuminates it; another bundle transmits an image back to the doctor for viewing. Loading… Lecture 2 Learning Objectives Describe the types of thin lenses Explain how to find the nature of image for thin lenses  Thin lenses A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Lenses are classified as diverging or converging, depending on what happens to the rays as they pass through the lens. A diverging lens bends light rays outward, away from the principal axis. A converging lens bends light rays inward, toward the principal axis. Thin lenses The principal axis of a lens passes through the centres of curvature of the lens surfaces. The optical centre of a lens is a point on the principal axis through which rays pass without changing direction. If the light rays passes through a converging lens, then they will converge to a point. This point is known as the focal point of the converging lens. If the light rays passes through a diverging, then the diverging rays can be traced backwards until they intersect at a point. This intersection point is known as the focal point of a diverging lens. The distance from the mirror to the focal point is known as the focal length (f). The radius of curvature (R)is the radius of the circular arc that most closely approximates the curve at that point in time. The focal length of a lens with spherical surfaces depends on four quantities: the radii of curvature of the two surfaces and the indices of refraction of the lens and of the surrounding medium (usually, but not necessarily, air). The Magnification and Thin Lens Equations Measurement of the Refractive Power of a Lens —“Diopter” The more a lens bends light rays, the greater is its “refractive power. "This refractive power is measured in terms of diopters. The refractive power in diopters of a convex lens is equal to 1 meter divided by its focal length. Thus, a spherical lens that converges parallel light rays to a focal point 1 meter beyond the lens has a refractive power of +1 diopter, as shown in Figure below. If the lens is capable of bending parallel light rays twice as much as a lens with a power of +1 diopter, it is said to have a strength of +2 diopters, and the light rays come to a focal point 0.5 meter beyond the lens. A lens capable of converging parallel light rays to a focal point only 10 centimeters (0.10 meter) beyond the lens has a refractive power of +10 diopters. The eye Learning Objectives Demonstrate the optics of the eye Explain the meaning of accommodation Explain how to correct the eye defects  The Parts of the Eye and Their Functions Dr Shahenaz Satti MBBS, MSc, PhD Learner Objectives Demonstrate the optics of the eye Explain the meaning of accommodation  Anatomy of the eye The wall of the eye consists of three concentric layers: The outer layer, which is fibrous, includes the cornea, corneal epithelium, conjunctiva, and sclera. The middle layer, which is vascular, includes the iris and the Choroid The inner layer, which is neural, contains the retina. The functional portions of the retina cover the entire posterior eye, except for the blind spot, which is the optic disc (head of the optic nerve.  Anatomy of the eye The ciliary muscle consists of : circular fibers longitudinal fibers, inserted near the corneoscleral junction, Suspensory ligaments from the ciliary muscle are joined to the zonule or lens ligament. The lens :is crystalline and biconvex, elongated epithelial cells and surrounded by a capsule  Functions of different parts of the eye Part Description Function Tough, transparent covering over the front Refracts light as it enters the eye (by a fixed Cornea part of the eye. Convex in shape. amount). Colored part of the eye that contains muscles. Iris Controls how much light enters the pupil. These relax or contract to adjust the size of the pupil. Allows light to pass through as it enters the Pupil Hole in the middle of the iris. eye. Refracts light to focus it onto the retina. The Transparent, bi-convex, flexible disc behind amount of refraction can be adjusted by Lens the iris. It is attached to the ciliary muscles altering the thickness and curvature of the by the suspensory ligaments. lens. Adjust the shape of the lens to make it more or Muscles connected to the lens by Ciliary muscles suspensory ligaments. less curved, so as to increase or decrease the refraction of light. Suspensory Connect the ciliary muscles to the lens and Slacken or stretch as the ciliary muscles contract or relax, to adjust the thickness and ligaments hold the lens in place. curvature of the lens. The lining of the back of eye containing two Contains the light receptors, which trigger types of light receptor cells. Rods are Retina sensitive to dim light and black and white. electrical impulses to be sent to the brain when light is detected. Cones are sensitive to colour. Component parts of the eye The optic nerve carries impulses from the retina to the brain You should be able to label and describe the functions of the main parts of the eye.  Optics of the eye Cont.. The lens system of the eye is composed of four refractive interfaces: I. Air and the anterior surface of the cornea 1.38 II. posterior surface of the cornea and the aqueous humor 1.33 III. aqueous humor and the anterior surface of the lens of the eye 1.44 IV. posterior surface of the lens and the vitreous humor.1.34 Reduced eye.” useful in simple calculations. a single refractive surface is considered to exist, with its central point 17 millimeters in front of the retina and a total refractive power of 59 diopters when the lens is accommodated for distant vision The lens system of the eye can focus an image on the retina. The image is inverted and reversed with respect to the object. However, the mind perceives objects in the upright position despite the upside- down orientation on the retina because the brain is trained to consider an inverted image as normal.  Mechanism of Accommodation At rest, the ciliary muscle is relaxed, and the suspensory ligament is under tension lens into a flattened shape. In accommodation, both the circular and longitudinal ciliary muscle fibers contract Ciliary body moves inward and forward relaxing tension on the suspensory ligament and allowing the elastic lens to become more convex. The increased convexity occurs mainly in the anterior surface of the lens. A number of diopters are added to the power of the lens, allowing light rays to be focused on the retina (up to 12 diopters in children).  Emmetropia (Normal Vision) Accommodation enables an eye to form a sharp image on the retina of objects at a range of distances from the near point to the far point. An adult with good vision has a near point at 25 cm or less and a far point at infinity. A child can have a near point of 10 cm or less. Optometrists write prescriptions in terms of the refractive power (P) of a lens rather than the focal length. The refractive power is simply the reciprocal of the focal length (P=1/f). Refractive power is usually measured in diopters (symbol D). One diopter is the refractive power of a lens with focal length f = 1 m (1 D = 1 m−1). The shorter the focal length, the more “powerful” the lens because the rays are bent more. Converging lenses have positive refractive powers, and diverging lenses have negative refractive powers. Myopia (nearsightedness) A myopic eye can see nearby objects clearly but not distant objects. Myopia (nearsightedness) occurs when the shape of the eyeball is elongated or when the curvature of the cornea is excessive. A myopic eye forms the image of a distant object in front of the retina. The refractive power of the lens is too large; the eye makes the rays converge too soon. A diverging corrective lens (with negative refractive power) can compensate for nearsightedness by bending the rays outward. Problem Without her contact lenses, Dana cannot see clearly an object more than 40.0 cm away. What refractive power should her contact lenses have to give her normal vision? Hyperopia (Farsightedness) A hyperopic (farsighted) eye can see distant objects clearly but not nearby objects; the near point distance is too large. The refractive power of the eye is too small; the cornea and lens do not refract the rays enough to make them converge on the retina. A converging lens can correct for hyperopia by bending the rays inward so they converge sooner. In order to have normal vision, the near point should be 25 cm (or less). Problem Winifred is unable to focus on objects closer than 2.50 m from her eyes. What refractive power should her corrective lenses have?  Summary Errors of Refraction Correction Normal Vision Farsightedness Nearsightedness Sound Chapter 12 Learning Objectives: Lecture 1 Define the sound waves and show the difference between longitudinal and transverse waves Explain the wave properties and tell what is the audible frequency Explain the wave equation and how to use it to calculate the speed of sound waves Explain the differences of speed of sound in different materials Show how the speed of sound changes with temperature Demonstrate the three parts of the human ear Lecture 2 Explain the medical imaging by ultrasound Explain what is doppler effect and its application in medicine Lecture 1 Define the sound waves and show the difference between longitudinal and transverse waves Explain the wave properties and tell what is the audible frequency Explain the wave equation and how to use it to calculate the speed of sound waves Explain the differences of speed of sound in different materials Show how the speed of sound changes with temperature Demonstrate the three parts of the human ear  Waves Two types of waves in nature; Transverse and Longitudinal waves In a transverse wave, the motion of particles in the medium is perpendicular to the direction of propagation of the wave. In a longitudinal wave, the motion of particles in the medium is along the same line as the direction of propagation of the wave. Longitudinal wave Transverse wave Waves Transverse waves can be recognised by their crests and troughs. Crest is the highest part of a wave and Trough is the lowest point of a wave. Longitudinal waves can be recognised by their compressions and rarefactions. Compressions the close together part of the wave Rarefaction is the spread-out parts of a wave. Wave charecteristics Wavelength (λ): Distance from a point on a wave to the same corresponding point on the next wave (expressed in meter) Frequency (f): Number of waves that pass a point in one second (expressed in Hz) Amplitude (A): The maximum distance the particles in a wave vibrate from their rest position (expressed in meter) Wave velocity (v): Velocity of wave in that medium. It depends on the type of wave and medium it passing through (expressed in m/s) Period (T): Time taken by a particle to complete one wave cycle (expressed in seconds) Period=1/frequency 1 𝑇= 𝑓 Frequency Ranges of Animal Hearing The human ear responds to sound waves within a limited range of frequencies. We generally consider the audible range to extend from 20 Hz to 20 kHz. The terms infrasound and ultrasound refer to sound waves with frequencies below 20 Hz and above 20 kHz, respectively. The audible ranges for animals can be quite different. Most mammals can hear frequencies much higher than we can. Dogs can hear frequencies as high as 50 kHz, which is why we can make a dog whistle that is inaudible to humans. Mice can produce and hear sounds with frequencies up to about 90 kHz, higher than what their predators can hear. Bats and bottlenose dolphins can hear frequencies above 100 kHz. Elephants and rhinoceros can hear frequencies down to about 14 Hz and 10 Hz, respectively. Speed of waves The distance moved by the wave in one second is the wave speed “v”. Wave speed = frequency x wavelength v= 𝒇𝝀 Sound waves travel faster as density of medium increases. Sound waves travel faster in solids than they do in liquids than they do in gases. vsolids > vliquids > vgases Speed of Sound in Gas The speed of sound in an ideal gas is proportional to the square root of the temperature (in Kelvin). 𝑣∝ 𝑇 The speed of sound in an ideal gas at any absolute temperature T (in K)can be found 𝑇 𝑣 = 𝑣0 𝑇0 where the speed of sound is v0 at a temperature T0 (in K). An approximate formula that can be used for the speed of sound in dry air (only) is v = 331.3 + (0.6)TC where TC is air temperature in degrees Celsius Problem The speed of sound in dry air (0% humidity) at 0°C (273.15 K) is 331.3 m/s. Find the speed of sound at 20°C (293.15 K)?  Parts of the Ear The ear is divided into 3 main parts: – Outer Ear – Middle Ear – Inner Ear  The Outer Ear Contains: pinna (lobe), ear canal, & ear drum.  The Middle Ear Contains 3 bones: hammer, anvil, & stirrup.  The Inner Ear Contains: cochlea and auditory nerve. Label the Parts of the Ear Outer Ear Hammer Anvil Stirrup Middle Ear Inner Ear Eardrum Cochlea Auditory Nerve Pinna Ear Canal  Steps to Hearing 1. Vibrations move through the outer ear canal and vibrate the eardrum. 2. The eardrum passes its energy through a chain of three tiny bones, the anvil, hammer, and stirrup, in the middle of the ear. 3. The anvil, hammer, and stirrup pass the energy onto the cochlea. 4. The vibrations activate hair cells and fluid inside the cochlea. 5. Electrical signals are sent to the brain through the auditory nerve. Lecture 2 Explain what is doppler effect and its application in medicine Explain the medical imaging by ultrasound  The Doppler effect The shift in frequency caused by motion is called the Doppler effect. It occurs when a sound source is moving at speeds less than the speed of sound. The Doppler effect Sound frequency received by the observer (f0)is 𝑣 − 𝑣0 𝑓0 = 𝑓 𝑣 − 𝑣𝑠 𝑠 v is the velocity of sound, v0 is the velocity of observer, vs velocity of source and fs is the frequency emitted by the source. vo and vs are positive in the direction of propagation of the wave (from source to observer) and negative in the opposite direction.  Ultrasound Imaging Ultrasound is a medical imaging technique that uses high frequency sound waves and their echoes. Any sound with a frequency above 20 kHz—that is, above the highest audible frequency—is defined to be ultrasound. Ultrasound today is commonly used in prenatal care. It is also used to examine organs such as the heart, liver, gallbladder, kidneys, bladder, breasts, and eyes, and to locate tumours. Working 1. The ultrasound machine transmits high-frequency (1 to 5 megahertz) sound pulses into your body using a probe. 2. The sound waves travel into your body and hit a boundary between tissues (e.g. between fluid and soft tissue, soft tissue and bone). 3. Some of the sound waves get reflected back to the probe, while some travel on further until they reach another boundary and get reflected. 4. The reflected waves are picked up by the probe and relayed to the machine. 5. The machine calculates the distance from the probe to the tissue or organ (boundaries) using the speed of sound in tissue and the time of each echo's return (usually on the order of millionths of a second). 6. The machine displays the distances and intensities of the echoes on the screen, forming a two-dimensional image like the one shown below. Advantage of ultrasound Ultrasound has no known adverse effects. Ultrasound images are captured in real time, so they are available immediately and can show movement. Regular imaging techniques (x-rays) detect the amount of radiation that passes through tissue but cannot resolve details at different depths. Low cost Doppler ultrasound Doppler ultrasound is a technique that is used to examine blood flow. It can help reveal blockages to blood flow, show the formation of plaque in arteries, and provide detailed information on the heartbeat of the fetus during labor and delivery. Problem A train whistle is blown by the driver who hears the sound at 650 Hz. If the train is heading towards a station at 20.0 m.s-1, what will the whistle sound like to a waiting commuter? Take the speed of sound to be 340 m.s-1.