Mar 2018 Physics Notes

14 Physics Notes

Physics: Branch of science dealing with the interaction of matter and energy. It can be classified as classical (mechanics, thermodynamics, etc.) and modern (“quantum” and “relativity theory”) physics.

Projectile Motion > Motion of a body thrown horizontally and affected by Earth’s gravitational pull > Trajectory is the path taken by an object in projectile motion

Basic and Derived Quantities > Basic Quantities: length, mass, time, electric current, temperature, amount of substance, luminosity > Derived Quantities: Quantities defined in terms of two or more of the basic quantities. Examples of which are velocity, acceleration, force and work. Scalar and Vector Quantities > Scalar: Has magnitude and unit only (e.g., distance, speed, time, energy) > Vector: Has magnitude, unit, and direction (e.g., displacement, velocity, force and acceleration) Different Forms of Energy Energy: Ability to do work  Kinetic Energy: Possessed by a moving body  Potential Energy: Energy of a body due to its position or shape a. Gravitational Potential Energy: Energy of an object due to its vertical separation from the earth’s surface b. Elastic Potential Energy: Energy in a stretched or compressed spring c. Electric Potential Energy: Energy of electrons inside an atom  Internal Energy: a.) random kinetic energy of atoms and molecules; b.) chemical energy due to bonds and interactions between atoms and molecules. Kinematics Motion: Change in position of a body Distance: Length covered by a body due to its motion Displacement: Distance with direction Speed: Speed (s) is the distance travelled (d) over time 𝑚 (t). The unit used is . 𝑠 𝒅 𝒔= 𝒕 Velocity: Vector quantity which is the ratio of displacement (x) over time (t). 𝒙 𝒗= 𝒕 Average Velocity 𝑽𝟏 + 𝑽𝟐 𝑽𝒂𝒗𝒆 = 𝟐 Acceleration: the rate of change in velocity with respect to time. ∆𝒗 𝒂= ∆𝒕 where: ∆𝑣 = 𝑣𝑓𝑖𝑛𝑎𝑙 − 𝑣𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∆𝑡 = 𝑡𝑓𝑖𝑛𝑎𝑙 − 𝑡𝑖𝑛𝑖𝑡𝑖𝑎𝑙

The key to analyzing Projectile Motion is to treat the xand y-coordinates separately. • The velocity in the x-coordinate is constant, thus zero acceleration in the x-axis • The acceleration in the y-coordinate is constant, 𝑚 acceleration due to gravity = 10 2 𝑠

1. Body Thrown Upward (Free-Fall) An object is given an initial upward velocity v1. While in flight, the ball is pulled downward by gravity. Therefore, there is deceleration until it reaches its maximum height. Upon reaching the maximum height, the object will momentarily stop, V = 0m, before it starts to accelerate down (free-fall). Force and velocity are opposite in directions, the speed of the object decreases up to the highest point of its flight. Then it falls downward with increasing velocity until it reaches the ground. 𝑚 The net force due to gravity is Fg = mag where ag =10 2. 𝑠

2. Body Thrown Horizontally As an object is thrown horizontally, an initial horizontal force, Fh is applied. Once the object is released no more horizontal force acts on it. But it maintains its horizontal velocity, vh. This object is being pulled downward by gravity so it moves vertically downward with acceleration 𝑚 due to gravity, ag =10 2. The vertical force is 𝑠 𝑭𝒗 = 𝑭𝒈 = 𝒎𝒂𝒈 Thus the object moves in two directions at the same time, both horizontally (y-axis) and vertically (x-axis). The resultant velocity is 𝒗𝑹 = 𝒗𝒚 + 𝒗𝒙 Uniform Circular Motion Consider an object of mass, m, while moving in a circular path at constant speed (Fc = mac). Relating the magnitude of the centripetal acceleration, ac, with the speed of the body and radius of the circular path R. ac =

𝒗𝟐 𝑹

Fc = mac = m

𝒗𝟐 𝑹

Forces and Interactions Force: push or pull. It is measured in unit of Newton. It is an interaction between two bodies or between a body and its environment.

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

15 Major Types of Forces Contact Forces  Normal Force: It is a force exerted on an object by any surface with which it is in contact. This force is always perpendicular to the said surface.

 Law of Motion and Mass (or Law of Acceleration): “An unbalanced force acting on an object will cause the object to accelerate in the direction of the force”. Acceleration is directly proportional to the net force and inversely proportional to its mass.  Law of Interaction: “For every action there is an equal but opposite reaction.” Stress and Strain

 Friction Force: A force exerted on an object parallel to the surface, in the direction that opposes sliding.

Elasticity: Property of matter that enables it to return to its original size and shape when the applied external force is removed Stress: A component of a force perpendicular to the area it acts on. It is mathematically written as: 𝑭𝒐𝒓𝒄𝒆 Stress = 𝑨𝒓𝒆𝒂

Strain: A measure of deformation, usually it is the object’s change in length, ∆l Hooke’s Law: Strain is directly proportional to the cause of deformation (stress). Hence,

Different Types of Friction Forces 𝑭𝑺 = 𝑭𝑵 𝝁 𝑺 Static Force Sliding/ Kinetic Force Rolling Force

Y =

𝑭𝒌 = 𝑭𝑵 𝝁 𝒌

𝑭𝒓 = 𝑭𝑵 𝝁 𝒓

 Tension: The pulling force exerted by a stretched rope or cord on an object to which it’s attached Long-range Forces  Electromagnetic Force: Attraction or repulsion between electric charges or magnetic poles. Coulomb’s Law of Magnetism 𝒒 𝒒 𝑭𝒆 = 𝒌 𝟏 𝟐 𝟐 𝒓

where k (Coulomb's constant) = 8.99×109 N m2 C−2 q1 and q2 = magnitudes of the charges r = distance between the charges  Gravitational Force: Attracts bodies toward each other. Law of Universal Gravitation 𝒎 𝒎 𝑭𝒈 = 𝑮 𝟏 𝟐 𝟐 𝒓

where G (gravitational constant) = 6.67 x 10-11

𝑁𝑚 2 𝑘𝑔 2

m1 and m2 = mass of bodies r = distance between the bodies Weight: The gravitational force that the earth exerts on the body. W= Mass (G) Where G = acceleration due to gravity Newton’s Laws of Motion  Law of Inertia: “Bodies at rest will remain at rest and bodies in motion will continue moving at constant speed in a straight line unless acted upon by a net force”. This law implies that objects will remain at rest or moving at a constant rate if the sum of all forces acting on them is zero.

𝑺𝒕𝒓𝒆𝒔𝒔 𝑺𝒕𝒓𝒂𝒊𝒏

=

𝑭 𝑨 ∆𝒍 𝒍𝒐

where: Y = Young’s Modulus of Elasticity l0 = the original length of the material ∆l = the change in length Young’s Modulus is a measure of the stretchability or compressibility of a material within its elastic limit. The higher Y is, the more elastic the material. Pressure: Perpendicular force acting on a unit surface. 𝑭 P= 𝑨

The unit of pressure is Pascal (Pa) 1𝑁 1 Pa = 2 𝑚

Increase in height causes decrease in air density. Increase in molecular collisions causes increase in pressure. Pascal’s Principle An external pressure exerted on a static, enclosed fluid is transmitted uniformly throughout the fluid. Archimedes’ Magnitude of buoyant force, FB, is equal to the weight of fluid displaced by the object. 𝑭𝑩 = 𝑽𝒘 𝑫𝒘 𝒈 Vw= volume of displaced water V = volume of the object Dw= density of water D = density of the object A body will float in a fluid if it is less dense than the fluid. Impulse and Momentum Momentum: Tendency of a moving object to continue moving and the difficulty encountered in reducing that motion 𝒑 = 𝒎𝒗 𝑚 where m is mass and v is velocity. The unit is 𝑘𝑔 ∙ . Impulse of a force on an object for a time t is: 𝑰𝒎𝒑𝒖𝒍𝒔𝒆 = 𝑭𝒕 The unit is N∙s

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

𝑠

16 > The relationship between impulse of a force and the change in momentum is given by 𝑭𝒏𝒆𝒕 = 𝒎 𝒗𝒇 − 𝒎𝒗𝒊 where 𝒗𝒇 is the final velocity and vi is the initial velocity. This states that the sum of the impulses of all forces acting on an object for a certain time is equal to the change in momentum of the object during that time.

On moving Charges in Vacuum 𝑭 = 𝒒∙𝒗∙𝑩 where: q = no. of charges; v = velocity =

Conservation of Momentum If no external force (like friction) acts on a body, the momentum of the body will not change. Let p = mv1 + mv2 (the momentum of the system before collision) where: m1 = mass of object 1; v1 = velocity of object 1 m2 = mass of object 2; v2 = velocity of object 2 Let p’ = m1 v1’ + m2v2’ (the momentum of system after collision) The law of conservation of momentum states that: ∆𝒑 = 𝒑𝟏 − 𝒑 = 𝟎 𝒐𝒓 𝒑′ = 𝒑

Factors of Induced Current  Relative velocity of the conductor and magnetic fields  The strength of the magnetic field.  Length of the conductor in the field  Current is produced when a potential difference between two points in a circuit exist.  Can magnetism induce current? This is shown by the following equation. 𝑽=𝒗 ∙𝑩 ∙𝑳 Note that the current (l) is proportional to voltage (V). Thus as current increases, v, B, and L increases. ∆𝒑 𝑽= 𝒕 The induced voltage is numerically equal to the rate of change of the magnetic flux. As the flux changes, current is induced.

Work, Power and Mechanical Energy Work: Done when a force causes displacement. The unit of work is joules. 𝑾 = 𝑭𝒙 Power: The rate at which work is done. ∆𝑾 𝑷= ∆𝒕 Kinetic Energy: 𝟏 𝑲𝑬 = 𝒎𝒗2 𝟐

where m = mass and v = velocity Potential Energy 𝑷𝑬 = 𝒎𝒈𝒉 where m = mass of the object, g = 10 of the object

𝑚 , 𝑠2

and h = height

Conservation of Mechanical Energy 𝑲𝑬𝟏 + 𝑷𝑬𝟏 = 𝑲𝑬𝟐 + 𝑷𝑬𝟐 𝟏 𝟏 𝒎𝒗𝟏2 + 𝒎𝒈𝒉𝟏 = 𝒎𝒗𝟐2 + 𝒎𝒈𝒉𝟐 𝟐

𝟐

Magnetic Field Magnetic field is a region in space where the magnet affects another magnet. Magnetic fields can affect currentcarrying conductors and moving charges in vacuum. On Current- Carrying Conductors If a current carrying conductor is in a magnetic field, it moves to a direction at right angle to both the direction of I and B Magnetic Force: Magnetic force (F) is maximized when current I and magnetic field directions are perpendicular to each other. The magnitude of the force F depends on the following: a) Current (I); b) Strength of magnetic field (B); c) Length of the conductor that lies in magnetic field (L). In equation, magnetic force is: 𝑭 = 𝑩 ∙ 𝑰 ∙ 𝑳

𝐿 𝑡

Electromagnetic Induction Current is induced when a conductor moves across a magnetic field or when a magnetic field moves with respect to a stationary conductor.

Wave and Energy Energy Transfer  Waves are classified as mechanical and electromagnetic waves. They either move in circular or straight motion.  There are two types of waves: o Transverse - Movement of the particles of the medium are perpendicular to the direction of the wave motion. o Longitudinal - Movement is parallel to the direction of the wave.  Waves have different characteristics o Wavelength: Distance between two corresponding points on a wave train. o Wave Frequency: Expressed in hertz which corresponds to the number of times the wave source completes a vibration in one second. o Period: Time it takes the wave source to make one complete vibration. It is the reciprocal of frequency. o Amplitude: Highest or lowest displacement from a wave’s equilibrium position. Increase in amplitude causes a transfer of more energy. o Speed: Directly proportional to frequency 𝑠 = 𝑓𝜆 Doppler Effect Occurs when the speed of the wave is greater than the speed of the source.

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

17 Overview: Sound vs. Light Sound Waves Light Waves Longitudinal Transverse Mechanical Electromagnetic Propagated with medium: Can be propagated without a medium: can be propagated in vacuum Gas(slowest) Gas (fastest) Liquid Liquid Solid (fastest) Solid(slowest) Sound Characteristics of Sound Waves o Loudness or Intensity: Loud sounds have greater amplitude o Pitch: Highness or lowness of sound o Quality: Distinguishes sounds from one another Light Reflection in Plane Mirrors The image is reversed in a plane mirror. The virtual image is of the same size as the object in front of the mirror. Reflection in Curved Mirrors A curved mirror has a vertex V, a center of curvature c, and a principal focus F. The focal length, f, is the distance from V to F. Summary of Lens and Mirrors Type of Image Diverging Mirror Convex Mirror Virtual,Upright,Reduced Diverging Lens Concave Lens Converging Mirror Concave Virtual,Upright,Enlarged Mirror Real,Inverted,Enlarged Real,Inverted,Same size Converging Lens Convex Lens Real,Inverted,Reduced

around a corner to help keep people from running into one another. Convex Mirror Uses: Sunglasses  Convex mirrors are used to make sunglass lenses. These mirrors help reflect some of the sunlight away from the wearer's eyes. Convex Mirror Uses: Vehicles  Convex mirrors are often found on the passenger sides of motor vehicles. These mirrors make objects appear smaller than they really are. Due to this compression, these mirrors to reflect a wider image area, or field of vision. Convex Mirror Uses: Security  Convex mirrors are often placed near ATMs to allow bank customers to see if someone is behind them. This is a security measure that helps keep ATM users safe from robbery of any cash withdrawals and helps keep ATM users' identity more secure. Convex Mirror Uses: Magnifying Glass  Two convex mirrors placed back to back are used to make a magnifying glass. Application of Concave Mirrors Concave Mirror Uses: Vehicle  Concave mirrors are used in vehicle headlights to focus the light from the headlight. The light is not as diffused and the driver can see better at night. Concave Mirror Uses: Light Concentration  Concave mirrors are used to focus light for heating purposes.(e.g. solar cooker) Application of Lens Convex Lens Uses: Eye defects  Convex lens are used in eyeglass prescribed for individuals with hyperopia (far-sightedness). Concave Lens Uses: Eye defects  Convex lens are used in eyeglass prescribed for individuals with myopia (near-sightedness). Refraction Bending of light at the boundary between different media. The index of refraction is: 𝒄 n= 𝒗

where n = index of refraction, c = speed of light 𝑚 (3 × 108 ), and v = speed of light in the medium 𝑠

Additional notes  When object is placed at an infinite distance, image is a point at F.  When object is placed at F, the image is at infinity. Application of Convex Mirrors Convex Mirror Uses: Inside Buildings  Large hospitals, stores and office buildings often use convex mirrors to allow people to see what is

Law of Reflection “It states that the angle of incidence is equal to the angle of reflection.” In symbols, Ɵi = Ɵr where: Ɵi – angle of incidence Ɵr – angle of relection The normal line is always drawn perpendicular with the reflecting surface. Angle of incidence and reflection is measured from the normal line. Multiple Reflection of Light When light hits reflecting surfaces several times, multiple images will be formed. If the angle between two reflecting surfaces such as mirror decreases, the number of images formed increases. To determine the number of images

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

18 that can be formed between two mirrors hinged together at an angle is 360 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒𝑠 = −1 𝜃 Where Ɵ = angle between two mirrors Refraction of Light Light bends when it travels obliquely from one transparent medium to another. Light is bent toward or away from the normal as it changes its speed when traveling through different optical media. A measure of how fast or slow light travels from one medium to another is called the index of refraction (optical density). 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛(𝑛) 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑎 𝑣𝑎𝑐𝑢𝑢𝑚 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 𝑐 = 𝑣 Index of refraction is a dimensionless quantity and its value is always greater or equal to 1 since light travels fastest in a vacuum than any other media. When the first medium has greater index of refraction than the second medium, light bends away from the normal. If medium 2 is denser than medium 1, light bends towards the normal. Snell’s law is the basic law of refraction that shows the relationship between the angles of incidence and refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 Where, n1 – index of refraction of the first medium n2 – index of refraction of the second medium Ɵ1 – angle of incidence Ɵ2 – angle of refraction Dispersion of White Light A separation of white light into several rainbow colors after passing a prism is called dispersion. Dispersion occurs because the indices of refraction are wavelength dependent (Nowikow et al., 2002) The speed of light in vacuum is the same for all wavelengths but the speed in a material substance is different for different wavelengths. Dispersion is the dependence of wave speed and index of refraction on wavelength. In most materials, light of longer wavelength has greater speed than light of shorter wavelength since the value of the index of refraction decreases with decreasing frequency and increasing wavelength. A ray of white light incident on a prism separates it to rainbow colors – R, O, Y, G, B, V. Red light is deviated least while violet light is deviated most since deviation (change in direction) produced by a prism increases with increasing frequency and index of refraction and decreasing wavelength. Total Internal Reflection Total Internal Reflection happens when the incident angle is greater than the critical angle, this is possible only when light travels from denser to less dense medium such as diamond to air. As the angle of incidence increases, the angle of refraction also increases since light bends away

from the normal from denser to less dense medium. When the critical angle is reached, the angle of refraction is along the interface of the two media which is equal to 90 degrees from the normal line. Using Snell’s Law. 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 𝑛1 sin 𝜃𝑐 = 𝑛2 sin 𝜃2 𝑛2 sin 𝜃2 sin 𝜃𝑐 = 𝑛1 𝑛1 −1 𝜃 = sin ( ) 𝑛2 Incident angle (Ɵi) is equal to the critical angle (Ɵ c) when the refracted ray moves parallel to the boundary when Ɵ 2 = 90O. One of the applications of total internal reflection is the used of the flexible pipe in fiber optics industry. Images can be transferred from one point to another resulting to multiple internal reflection using the bundle of parallel fibers in constructing transmission line. Another application is seen in the medical field, physician utilize optical fiber devices to examine internal organs of the body or to perform surgery without making large incisions. Electrical wirings such as copper wiring and coaxial cables are being replaced by optical fibers since these can carry greater volume of telephone calls or other forms of communication (Serway, 2004) Diffraction of Light It is the bending of light waves around the objects it passes and spreads out after passing through the narrow slits which give rise to a diffraction pattern due to interference between light rays that travel different distances (Giancolli, 200_). When light passes through an opening that is large compared with the wavelength of light, a shadow will be caste on the screen with sharp boundary between the dark and light areas of shadow. But when light waves pass through thin silt, it diffracts which produces bright and dark areas. Longer waves diffract more since the amount of shadow depends on the wavelength of the wave compared with the size of the obstruction that casts the shadow (Hewitt, 2006). Interference of Light Interference of wave is the meeting or superimposing of one wave on another wave. Types of interference:  Constructive Interference – At points where the waves arrive in phase. As seen from the figure at the right, when a crest meets another crest or a trough meets another trough (waves are in phase), the resulting wave is being reinforced forming a supercrest or supertrough.  Destructive Interference – At points where the waves arrive in opposite phase. Figure at the right shows the meeting of waves with the same amplitude which are out of phase (crest meets trough) resulted to a cancellation of wave. Light is a transverse electromagnetic wave which exhibits interference. Striped Interference pattern was produced when a monochromatic light passes through closely spaced – slits. Series of bright and dark lines results from the different path lengths from the slits to the screen. The

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

19 central bright fringes are the results of the in phase waves that reinforced each other (Constructive Interference) while the dark fringes are produced from the meeting of the waves that are out of phase (Destructive Interference). Polarization of Light Polarization of light waves shows that light is really a transverse wave. All EM waves exhibits polarization. There are many applications of polarized light such as: a. Polarized light is useful in determining the size and shape of virus. b. Polaroid is a trademark for glare – reducing plastic which is used in sun glasses. Polaroids cut down the horizontally polarized light to reduce the glare and intensity. c. Polaroids with perpendicular axes are used in special types of glasses for three dimensional viewing (3-D view) d. Photo elastic stress analysis uses polarized light. Polarization by Transmission It is the most common method of polarization which utilizes Polaroid filter that blocks one of the two planes of vibration of an electromagnetic wave upon transmission of the light through it. Unpolarized light vibrates in all directions. Vertical and horizontal components of light have equal intensities but after passing through a polarized, one of the components is eliminated and light intensity is reduced to half. Unpolarized light can be entirely stopped when the two polaroids are crossed having perpendicular polarizing axes (Polarizer and Analyzer). The second Polaroid, the analyzer, then eliminates this component since its transmission axis is perpendicular to the first. You can try this with Polaroid sunglasses. Note that Polaroid sunglasses climinate 50% of unpolarized light because of their polarizing property: they absorb even more because they are colored. Polarization by Reflection When light strikes a nonmetallic surface at any angle other than perpendicular, the reflected beam is a polarized preferentially in the plane parallel to the surface. Furthermore, the component with polarization in the plane perpendicular to the surface is preferentially transmitted or absorbed. People who go fishing wear polaroid sunglasses to see beneath the water more clearly since it eliminates the reflected glare from the surface (Giancolli). Reflection of light off of non-metallic surfaces results in some degree of polarization parallel to the surface. Polarization by Refraction Refraction is the bending of light as it passes obliquely from one transparent medium to another. Light ray bends which acquires some degree of polarization. As light enters a transparent medium such as Iceland spar, it refracts the incident light into two different paths which are polarized. The double refraction of light can produce two images.

The two refracted rays passing through the Iceland Spar crystal are polarized with perpendicular orientations. Polarization by Scattering As light strikes the atoms of a material, the electrons of the atoms set into vibration which later produce their own electromagnetic wave radiated outward in all directions. The newly generated wave strikes other neighboring atoms that forces their electrons to vibrate at same original frequency, and then produces new electromagnetic waves radiated outward in all directions. The absorption and reemission of light waves causes the light to be scattered and partially polarized about the medium. Polarization by scattering is observed as light passes through our atmosphere which often produces a glare in the skies. Geometric Optics Images can be formed either by reflection of light as it hits an opaque or transparent medium respectively. The image formation can be illustrated by ray diagrams in geometric optics and can also be proven mathematically using the mirror or thin lens equation and magnification. Some important quantities/terms needed in the image formation by lens or mirror.  Object distance (do) – distance of the object from the mirror/lens.  Image distance (di) – distance of the image from the mirror/lens.  Focal length (f) – half of the radius of curvature (R) of the reflecting or refracting surfaces; the distance between the center of the mirror/lens to the focal point (F)  Focal point (F) – the point where incident parallel rays to come to a focus after reflection/refraction  Principal Axis – straight line perpendicular to the flat or curved reflecting or refracting surfaces  Magnification (M) – dimensionless quantity which tells whether the image formed is maximize, diminish or same size as the object.  Image size (h’) – size of the image  Object’s size (h) – size of the object To determine the location of the object or image, a mirror/thin lens equation is used. 1 1 1 = + 𝑓 𝑑𝑜 𝑑𝑖 Images formed by a mirror/lens can be real or virtual, erect or inverted. Real images are usually inverted while virtual images are erect/  Real images is formed when light rays pass through and diverge from the image point and can be displayed on the screen.  Virtual image do not pass through the image point but only appear to diverge from that point and cannot be displayed on the screen.  Erect image is an image formed in upright position.  Inverted image is an image formed which turns upside-down. Images can also be diminished, maximized or same size as the object.  Diminished image is the image formed that is smaller than the object.  Maximized image is the image formed that is larger than the image.

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

20 

Same size image is the image formed that is similar to the size of the object. According to the magnification formula (M): −𝑑𝑖 ℎ′ 𝑀= = 𝑑𝑜 ℎ When the absolute value of  M = 1, object is same size as the image  M < 1, diminished image  M > 1, maximize image In solving for the different unknowns, some sign conventions are important to remember to determine the kind of image that will be formed after reflection of light from mirror and refraction of light from lens. Sign Conventions for Mirrors and Lenses Description of Image Virtual or Focal Erect or Real Same/Max/Dim Length Inverted Image Real (positive Inverted Same (M = 1) Converging di) (negative h’) Max (M > 1) (+) Virtual Erect Dim (M < 1) (negative (positive h) di) Virtual Diverging Erect (negative Dim (M < 1) (-) (positive h) di) Eye is the most remarkable optical device necessary to see the things around us in the presence of the visible light spectrum. It is also similar to a camera that focuses light and produces a sharp image. Camera-Eye Analogy  Lens – Cornea/Lens  Aperture – Pupil  Film – Retina  Shutter - Eyelid Eye Defects Farsightedness (Hyperopia): is the inability to see nearby objects clearly. Since the images is formed behind the retina, a converging lens is needed to correct this eye defect. In order to focus the image on the retina, the converging lens refracts more the incoming rays toward the principal axis before entering the eye. Nearsightedness (Myopia): is the inability to see far objects clearly. Since the image is formed in front of the retina, a diverging lens is needed to correct this eye defect. In order to focus the image on the retina, the diverging lens refracts more the incoming rays toward the principal axis before entering the eye. Old-age vision (Presbyopia): it is due to a reduction in accommodation ability as the ciliary muscle weakens and the lens hardens. The cornea and lens do not have sufficient focusing power to bring nearby objects into focus on the retina. Converging lens can be used to correct this eye defect.

Astigmatism: when the cornea or the lens or both are not perfectly symmetric, this resulted to an eye defect that prevents the light rays from meeting at a single point, producing an imperfect image. In order to correct this eye defect, lenses with different curvatures in two perpendicular directions can be used. Light and Colors White light is not a color rather it is the presence of all frequencies of visible light while Black is the absence of the visible light spectrum. White is capable of reflecting all visible light spectrum white and black is capable of absorbing all visible light spectrum and converted it to heat energy. When the colors of light with varying degrees of intensity are mixed/added, another color will be produced. Primary Colors of Light 1. Red (R) 2. Blue (B) 3. Green (G)

Secondary Colors of Light 1. Yellow (Y) = R + G 2. Cyan (C) = B + G 3. Magenta (M) = B + R

White light can also be formed when the three primary colors with same intensity are added. W=R+B+G Complementary Colors of Light 1. Red + Cyan = White 2. Green + Magenta = White 3. Blue + Yellow = White The color of objects is not in the object but rather in the light which reflects off or transmits through the object. In color subtraction, the ultimate color appearance of an object is determined by beginning with a single color or mixture of colors and identifying which color or colors of light are subtracted from the original set. W – B = (R + G + B) – B = R+G=Y The object is capable of absorbing Blue under the White light. The object appears Yellow to the observer since blue light was cancelled and transformed to heat energy. R–B=R The object is capable of absorbing Blue under the Red light. The object appears Red to the observer since blue light cannot be cancelled and transformed to heat energy from Red light. M – B = (R + B) – B = R The object is capable of absorbing Blue under the Magenta light. The object appears Red to the observer since blue light was cancelled and transformed to heat energy. Electromagnetic Wave Electromagnetic waves consist of a changing electric field and a changing magnetic field. James Clerk Maxwell (1831-1879) theorized that electromagnetic induction happens in space even without the presence of a conductor.

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER

21 Electromagnetic Spectrum

Ohm’s Law Current is directly proportional to voltage and inversely proportional to resistance. 𝑽 = 𝑰𝑹 where V = voltage, I = current, and R = resistance Note: Ohm’s law applies only to metallic conductors and not to transistors or electrolytes.

Nature of Matter and Energy The photon’s having energy and momentum is expressed by 𝑬 = 𝒉𝒇 where h=Planck’s constant(6.63x10-34J-s) and f= frequency 𝒉𝒇 𝒑= =𝒉𝝀 where p = the momentum

𝒄

Radioactivity The spontaneous emission of radiation from the nuclei of atoms of certain substances termed as radioactive. Radiation is of three main types: alpha (fast-moving helium nuclei); beta (fast-moving electrons); gamma (high-energy, highly penetrating protons). Beta and gamma radiation are both damaging to body tissues, but are especially dangerous if a radioactive substance is ingested or inhaled. When radiation takes place, there is loss of energy. Electricity Electromagnetic Energy Circuit: Any arrangement of materials that permits electrons to flow. It is composed of a source of electrical energy, load, and connecting wires. Electric Current: The net flow changes along a material. The unit used is ampere. The electron charge’s unit is coulomb. In equation form, electric current is: 𝒒 I=

Factors of Wire Resistance o Length of Material: Longer path for electric current results to greater resistance o Wire Diameter: Greater cross-sectional area of conductor results to lesser resistance. o Kind of Material o Temperature: Higher temperature results to greater resistance. o Resistivity: Ability of the substance to conduct electric current. The resistance is equal to the product of resistivity and length of wire divided by its cross-sectional area. 𝝆𝑳 𝑹= 𝑨 where L = length of conductor and A = cross-sectional area of the conductor, and ρ (rho) = resistivity of the material. Electrical Power and Energy Power Input: Rate at which an appliance uses up electrical energy. It is measured in watts. 𝑷 = 𝑽𝑰 Circuits Series Circuits: Current passes to only one route from the source through the several loads and back to the source. The current is the same in every part of the circuit. Parallel Circuits: General loads are connected to the same voltage source and current is divided among these loads.

𝒕

where I = electric current, q = number of charges passing through a perpendicular cross section of a conductor, and t = time 𝑐𝑜𝑢𝑙𝑜𝑚𝑏 1 ampere = 1 𝑠𝑒𝑐𝑜𝑛𝑑

6.3 x 1018 electrons pass a cross-section of a conductor in 1 second. Voltage: Potential difference between points when work 𝐽 is done to move charge between points. The unit is . 𝐶

In equation form,

Voltage (VT) Current (IT) Resistance (RT)

Series V1 + V2 + … + Vn

Parallel V1 = V2 = … = Vn

I1 = I2 = … =In

I1 + I2 + … +In

R1 + R2 +...+ Rn

𝟏 𝟏 𝟏 𝟏 + +⋯ 𝑹𝟏 𝑹𝟐 𝑹𝒏

Diagram

𝑾 𝑽= 𝒒 Resistance: Tendency of the unit to resist the passage of electric current. The unit is ohm (Ω).

LEARNFAST REVIEW AND TUTORIAL HUB – NMAT REVIEWER