Other Physics

Question 1

Torque

Answer 1

Measure of a force’s ability to cause rotational acceleration
If force acts at any point on an object other than the center of mass, object accelerates rotationally
/tau = F r sin\theta
Torque is a vector (can be clockwise or counter-clockwise)
Where r is position of force application to the point of rotation
When l is lever arm, force is applied perpendicularly to r and sin \theta = 1
Greater the net torque on an object, greater the acceleration

Question 2

Work

Answer 2

W = Fd
In units of Joules = Newton meters
Useful simplification of thermodynamic equations for MCAT when no friction:
W + q = \delta K + \delta U

Question 3

What are the ways energy can be divided?

Answer 3

Energy can be divided into mechanical and non-mechanical energies
Mechanical energy (\delta Em): energy of a macroscopic system
- Potential energy: energy of position
- Kinetic energy: K = 1/2 mv^2, energy of motion

Question 4

Power

Answer 4

Rate of energy transfer

P = W/t = \delta E / t = Fd cos \theta / t = Fv cos \theta (theta is angle between F and v)

Question 5

Law of Conservation of Mechanical Energy

Answer 5

When only conservative forces are acting, the sum of mechanical energies remains constant
K1 + U1 = K2 + U2 (conservative forces only, no heat)
Conservative force: if mechanical energy prior equals mechanical energy after, conservative force, force must be a function of position only

Question 6

What are some example of conservative vs. non-conservative forces?

Answer 6

Conservative forces: gravitational energy, elastic potential energy of a spring
Non-conservative forces: kinetic frictional forces, pushing and pulling forces of humans or animals, sum of potential and kinetic energies remains constant
Except for frictional forces, work done by all non-conservative forces = change in mechanical energy of systems upon which they are applied
W = \delta K + \delta U
Technically speaking, a conservative force does not do work bc energy is never gained or lost by the system

Question 7

Mechanical advantage

Answer 7

The ability to reduce applied force required to do a given amount of work
- Machines are able to reduce force, but do not change work

Question 8

Ramp

Answer 8

Inclined plane that reduces force needed to do work by increasing distance over which force is applied (think about W = Fd)
Force needed is only mg sin\theta instead of mg to lift an object to top of ramp (by sliding on ramp instead)
E.g. to reduce the force to 1/2 mg, make a ramp that is 2h long
Length of ramp calculated by: h/sin \theta
We can see that work, W = mg sin\theta x h / sin \theta = mgh, and did not change

Question 9

Lever

Answer 9

Beam attached to fulcrum (pivot point)
Reduces force needed to do a given amount of work by increasing distance over which the force is applied (similar to ramp)
- Based on principle of torque, and remember work is always the same
- Doubling the length of the lever arm reduces the force required by a factor of two
Torque = F x L
If lifting mass, then balance the torques of two ends of the lever:
- torque1 = mg x L1, torque2 = F x L2
- F = mg L1 / L2

Question 10

Pulley

Answer 10

Allows force to act over a greater distance so that the same amount of work can be done with less force

• Uses rope to increase distance over which the force acts
• Magnitude of force acting throughout the length of rope is called tension
• Tension is scalar and has no direction, assume that tension throughout a rope is constant (same at every point), means ideal pulley

Question 11

Specific Gravity

Answer 11

Symbol SG = \ro_substance / \ro_water
Specific gravity less than 1 indicates substance lighter than water
\ro_water = 1000 kg/m^3 = 1 g/cm^3

Question 12

Fluid pressure

Answer 12

Pressure experienced by object as a result of impulse of molecular collisions
It is average of magnitudes of change in momentum of collisions divided by time duration of collisions
P = F / A = \ro g y (for fluid at rest with uniform density in sealed container)
SI unit is Pascal, a scalar quantity
Fluid at rest experiences only forces perpendicular to surface

Question 13

How can the total pressure of a column of different fluids be found?

Answer 13

Adding the pressures due to each fluid:
Ptotal = \ro_1 g y_1 + \ro_2 g y_2 + \ro_3 g y_3 + …
Must add atmospheric pressure if the container is open to the air as well
In any fluid open to atmosphere:
P = \ro g y + Patm
At sea level, Patm = 101,000 Pa = 1 atm

Question 14

Pascal’s principle

Answer 14

Pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished through teh fluid

Question 15

Gauge Pressure

Answer 15

Amount by which a system’s pressure deviates from atmospheric pressure
Pabs = Pgauge + Patm
Absolute pressure: pressure of a system relative to a vacuum

Question 16

Hydraulic Lift

Answer 16

Simple machine that works via Pascal’s principle
Two pistons and a container enclose a standing incompressible fluid
Force applied on piston with less area, which gets transferred undiminished to piston 2 which has greater area, therefore translating to greater force (does not change work)
Distance compressed at piston 1 is greater than distance travelled at piston 2

Question 17

Buoyant force

Answer 17

Standing fluid exerts this force on any object that is floating, submerged, or sunk in the fluid
Both pressure and force increase with depth, causing an object in fluid to experience both greater pressure and greater force at points farther from fluid’s surface (object experiences upward force)
The difference in pressure (and therefore force) experienced by points closest to and farthest from the water surface (on the same object) creates upward buoyant force
Since the lower surface of a fully submerged box experiences greater pressure on the surface than the upper surface of a fully submerged box, it experiences a net upward force

Question 18

Archimede’s Principle

Answer 18

F_B = \ro_fluid V_fluid g = (m_fluid / V_fluid)(V_fluid) g = m_fluid g, V_fluid is volume of fluid displaced
Upward buoyant force is equal in magnitude to weight of displaced fluid

Question 19

How do you compute the fraction of an object that will be submerged in water?

Answer 19

Fraction submerged = \ro_object / \ro_fluid = V_fluid / V_object

Floating object:
F_B = \ro_fluid V_fluid g = m_fluid g = F_G = m_object g
Simplifies to m_fluid = m_object because floating object displaces a volume of fluid with a mass equal to its own mass
Object only floats when density is less than density of fluid on which it floats

Question 20

Case of submerged object

Answer 20

If upward buoyant force equals downward force of gravity when \delta y are their maximum values, object is submerged
Submerged object is like a floating object that does not sink, but entirety of submerged object is within the fluid
m_fluid = m_object, V_fluid = V_object
\ro_fluid must equal \ro_object
F_B = \ro_fluid V_fluid g, F_g,object = \ro_object V_object g

Question 21

Case of the sunk object

Answer 21

Sunk object displaces a volume of fluid equal to its own volume and experiences upward buoyant force that is less than downward gravitational force
Experiences net downward force that causes object to accelerate downward until it contacts a surface able to provide enough upward normal force to counter downward force of gravity
F_B < F_G, m_fluid < m_object, but V_fluid = V_object
F_B + F_N = F_G = m_object g, apparent weight is equal to difference between downward force of gravity and upward buoyant force

Question 22

What is the apparent weight loss of an object?

Answer 22

\ro_fluid / \ro_object = m_fluid / m_object since volumes are equal
\ro_fluid / \ro_object x 100% = apparent weight loss of object

Question 23

Center of buoyancy

Answer 23

Buoyant force acts at an object’s center of buoyancy, which is the point where the center of mass would be if the object had uniform density
If object is not uniformly dense, center of mass and center of buoyancy are not at the same place (resulting in torque)

Question 24

What are the two types of fluid motion?

Answer 24

Random translational motion: contributes to fluid pressure as in a fluid at rest
Uniform translational motion: shared equally by all molecules at given location in fluid, does not contribute to fluid pressure
Some of random translational motion can be converted to uniform translational motion and vice versa

Question 25

How do ideal fluids vary from real fluids?

Answer 25

1. Have no viscosity: measure of fluid’s temporal resistance to forces that are not perpendicular to it surface - Related to drag: force similar to friction that is created by viscosity and pressure due to motion 2. Ideal fluids are incompressible with uniform density 3. Ideal fluids lack turbulence; experience steady (or laminar) flow, meaning that all fluid flowing through any fixed point has same velocity (turbulence: velocity at any fixed point in fluid may vary with time) 4. Ideal fluids experience irrotational flow; where any object moving with an ideal fluid will not rotate about its axis, but will continue to point in one direction

Question 26

Continuity Equation

Answer 26

Q = Av = Ad / t v= d / t Q is volumetric flow rate

Question 27

Mass flow rate of fluid

Answer 27

Mass flow rate is I I = \ro Q = \ro A v Where v is velocity, A is cross-sectional area Area inversely proportional to velocity

Question 28

Bernoulli’s equation

Answer 28

Restates conservation of energy in terms of densities and pressures, the intensive properties used to describe fluids Sum of pressure, kinetic energy per unit volume, and potential energy per unit volume of fluid remain constant through that fluid P1 + (1/2)\ro v1^2 + \ro g h_1 = P2 + (1/2) \ro v2^2 + \ro g h2 Where h is distance above some arbitrary point (as compared to y which is distance beneath surface of fluid) Multiplying any of the terms in Bernoulli’s equation by volume gives units of energy Energy is conserved in ideal fluid flow so total energy must remain constsant

Question 29

If water in a container at rest gets released from a spigot at a height of 0 and all the potential energy is converted into kinetic energy, what is the equation for the velocity of the water?

Answer 29

v= sqrt(2gh)

Question 30

Pitot tube

Answer 30

Horizontal tube with U-shaped opening, one exposed to fluid and one exposed to air on other side Difference in height of mercery in U-shaped tube can be used to get pressure difference between fluid facing side and non-fluid facing side P2 + 1/2 \ro v2^2 = P1 OR 1/2 \ro v2^2 = P1 - P2 = \delta P Velocity is then: v2 = sqrt(2 \delta P / \ro_fluid)

Question 31

What is the relationship between pressure and velocity in ideal fluid flow?

Answer 31

Assuming constant height, as velocity increases, pressure decreases Increase in velocity corresponds to increase in kinetic energy and if no change in potential energy (no change in height), then pressure must decrease

Question 32

Venturi tube

Answer 32

Horizontal tube with constricted region- region with decreased cross-sectional are in middle Can be used to determine velocity of a fluid that is flowing with it in contrast to pitot tube which determines velocity of tube flowing past it - Bernoulli equation states that for fluid at constant height, decrease in cross-sectional area corresponds to increase in velocity, and increase in velocity is associated with decrease in pressure

Question 33

What are the differences of the behavior of an ideal to non-ideal fluid?

Answer 33

Drag and viscosity are like firction and always act to impede flow - occurs at fluid-object interface and is a force working against flow - As move away from fluid-object interface, effect of drag lessens - Fastest moving fluid in pipe is towards center, away from pipe walls - Resistance to flow increases as length of pipe increases Fluid does not necessarily move form high pressure to low pressure, driving force is fluid’s tendency to move such that entropy increases

Question 34

POiselle’s Law

Answer 34

Q = \delta P (pi r^4) / (8 \eta L) - predict flow rate of REAL fluid In real fluid of blood, decreasing area of vessel doesn’t necessarily mean faster flow, due to interactions of various components of blood resulting in drag forces that are not present in ideal fluids (blood clot), although this does not mean that velocity does not increase to some extent

Question 35

Surface tension

Answer 35

Describes the intensity of intermolecular forces of a fluid per unit length - Responsible for formation of droplets - intermolecular forces pull inward, minimizing surface area by creating a more spherical shape - Affected by temperature of fluid, higher temperature leads to weaker surface tension

Question 36

Coulomb’s law

Answer 36

F = k (q1 q2 / r^2) Where k is Coulomb’s constant (k = 8.988 x 10^9 N m^2 / C^2), q represents respective charges, r is distance between centers of charge

Question 37

Electric field

Answer 37

``` Electrostatic force per unit charge Symbol, E E = k q1 / r^2 Units N/C or V/m Electric field for a system of point charges is found by summing fields due to each charge ```

Question 38

What is the force on a charge in an electric field? The potential energy?

Answer 38

F = q E is force U = qEd is potential energy (d is displacement measured from a zero point of our own choosing) If electric field is created by point charge, potential energy is: U = k q1 q2 / r

Question 39

Voltage

Answer 39

Potential for work by an electric field in moving any charge form one point to another V = Ed Units: volts (V), or J / C Voltage due to a point charge: V = k q1 / r Scalar value, so can sum voltages due to each individual charge in a group of point charges

Question 40

Equipotential surfaces

Answer 40

Surface normal to the electric field that describes a set of points all with the same potential Can be drawn at any point in the field

Question 41

Electric dipole moment

Answer 41

Created by two opposite charges with equal magnitude p = q d, vector whose magnitude is charge q on one of the charges multiplied by distance d between the charges In physics, vector points in opposite direction to electric field (negative charge to positive charge)

Question 42

Resistance

Answer 42

Quantitative measure of object of particular shape and size to resist flow of charge is called resistance (R) measured in ohms R = \ro L / A Where \ro is resistivity, a measure of the substances tendency to resist flow L is the length of the wire, and A is cross-sectional area Resistance can also vary with temperature according to equation: R= Ro [1 + alpha(T - To)], where Ro and To are resistance and temperature at some reference value and alpha is a constant specific to material in substance - increase in temperature of material increases resistsance

Question 43

Capacitor

Answer 43

Used to temporarily store energy in a circuit - stores it in the form of separated charge - in parallel plate capacitors, two plates made from conductive material are separated by a very small distance - charged capacitor: one plate holds positive charge, other plate holds exact same amount of negative charge, creating an electric field that is constant everywhere between the plates E = (1/K) (Q / A \epsilon_0), where K is dielectric K, Q is charge on either plate, and epsilon_0 is derived from Coulomb’s constant k = (1/ 4 pi \epsilon_0)

Question 44

Capacitance

Answer 44

C = Q / V = K (A epsilon_0) / d In a parallel plate capacitor, amount of charge that can be stored is directly proportional to area of each plate - because charge sits on surface of plates - increasing thickness of capacitor will not increase ability to store charge - As voltage is defined by distance (V = Ed), the farther the plates are separated, lower the capacitance

Question 45

What is the energy stored in a capacitor?

Answer 45

U = 1/2 Q V = 1/2 C V^2 = 1/2 Q^2 / C

Question 46

Dielectric constant, K

Answer 46

Refers to the substance between the plates of a capacitor - substance between the plates must be an insulator, or it would conduct electrons from one plate to the other and charge could not be built up - acts to resist creation of an electric field, allowing capacitor to store more charge K of a vacuum is defined to be 1 (air is close to one and all other constants increase from there)

Question 47

How do we compute the effective resistance of resistors in series and in parallel? What about capacitors?

Answer 47

For resistors in series: Rtotal = R1 + R2 + ... For resistors in parallel: 1/Reff = 1/R1 + 1/R2 + ... For capacitors in series: 1/Ceff = 1/C1 + 1/C2 +... (like a single capacitor with a distance between plates equal to distance between first plate of 1st and 2nd plate of last) For capacitors in parallel: Ceff = C1 + C2 + ... (single capacitor with plate area equal to sum of areas of capacitors)

Question 48

Magnetic field

Answer 48

Concurrent with an electric field All charges, static and moving create an electric field around them, only moving charges produce magnetic fields - static electric field produces no force on a magnet, and magnetic field produces no force on a static electric charge - magnetic poles never found in isolation, north and south always accompany each other - magnetic field measured in Teslas (T) - lines of force in magnetic field point from north pole to south pole of magnet that created the field

Question 49

What is the magnitude of the force on a charge moving with velocity v through a magnetic field?

Answer 49

F = q v B sin \theta Theta is angle between magnetic field and velocity of the charge B is magnetic field, q is charge

Question 50

Can work be done by a magnetic field?

Answer 50

Magnetic force is always applied at 90 degrees to velocity of the particle and cos(90 deg) = 0, so no work can ever be done by this force: W = Fd cos \theta = 0 Cannot transfer energy to the particle, so cannot change speed of particle

Question 51

What does the velocity of a wave depend on?

Answer 51

Constant for a particular medium 1. Medium’s elasticity, or resistance to change in shape 2. Medium’s inertia, or resistance to change in motion v = sqrt ( B / \ro), where B is bulk modulus of a medium (measure of elasticity) and \ro is density of medium is measure of inertia v = sqrt ( gamma RT / M) if temperature is changing in gas, gamma is constant for a specific gas that compensates for temperature changes during contractions, M is molecular mass

Question 52

What happens as a wave moves from one medium to another?

Answer 52

Frequency of wave does not change, but velocity does change according to characteristics of new medium Increase in elasticity as compared to old medium will increase velocity of wave - elasticity increases as intermolecular attraction between molecules increases and inertia increases as mass and density increase Increase in inertia as compared to old medium will decrease velocity of wave

Question 53

Compare the velocity of a wave traveling in a solid vs. a liquid vs. a gas

Answer 53

Velocity of a wave in a solid > velocity of wave in liquid > velocity of wave in gas

Question 54

Intensity of a sound wave

Answer 54

Average rate of energy transfer per unit area - depends on density of medium, wave frequency, and wave velocity - I = 2 pi^2 \ro f^2 A^2 v, \ro is density of medium, f is wave frequency, A is amplitude, v is wave velocity Measured in W / m^2

Question 55

Intensity level

Answer 55

Measure of loudness \beta = 10 log I / I_0 Units are decibels Normal threshold of hearing is 10^-12 W / m^2 What we can and cannot hear depends on frequency and intensity (20 - 20k Hz)

Question 56

What happens when a wave reflects off a medium that is denser? Less dense?

Answer 56

When a wave reflects off a medium that is denser, it is inverted - experienced a phase shift When a wave reflects off a medium that is lighter, it remains upright

Question 57

Resonance

Answer 57

Condition where the natural frequency and driving frequency are equal

Question 58

Standing wave in pipe

Answer 58

Pipe open at both ends: nodes are in the middle of the pipe and ends are antinodes Lambda = 2L / n, so L = lambda / 2, L = lambda, L = 3 lambda / 2 Pipe closed at one end: node at closed end, lambda = 4L / n, so L = lambda /4, L = 3 lambda / 4 Always longitudinal wave (represented by transverse wave)

Question 59

Standing wave in string

Answer 59

Each end in which string is attached to wall is a node Lambda = 2L /n Always transverse wave

Question 60

Attenuation

Answer 60

Decrease in intensity of a wave propagating through a medium - Causes of attenuation are reflection, spreading (scattering), and absorption - Attenuation of sound waves due to reflection makes it difficult to create ultrasonic images of a bone’s interior - Recall that intensity depends on square of frequency and amplitude and the density of medium and wave velocity, however frequency is determined by wave source, so amplitude and velocity decrease

Question 61

Doppler effect

Answer 61

Change in perceived frequency that occurs when wave source and observer move towards or away from each other - when source or observer is moving toward the other, observed frequency is higher than source frequency - If wave is sound, observer hears different pitch, if wave is light observer observes different color than was emitted Equation: fo = fs (c +- vo) / (c -+ vs) To determine sign to use, think about direction source is moving first. If source is moving towards observer, use negative, if observer moving in same direction then use same sign, if not then use opposite sign

Question 62

Beats

Answer 62

Occur when two waves with slightly different frequencies are super-imposed - Some points they will be nearly in phase and experience constructive interference - Other points they will be out of phase and experience destructive interference - Points will alternate at beat frequency, or frequency equal to difference between frequencies of original two waves f_beat = | fo - fs | Plug in: f_beat / fs = 2v / c (Doppler shift has occurred twice in Police radar speed detecting scenario)

Question 63

Shock wave

Answer 63

Conical wave front, produced when velocity of sound source exceeds velocity of sound wave, consists of oscillations between high and low pressures - Mach number: Ratio of velocity of source to velocity of wave vs / v - Mach number increases as velocity of sound source increases - When source moves faster than speed of sound, many wave fronts overlap, generating region of very low air pressure ( air moves in response to pressure gradient, and rapid movement creates loud sonic boom)

Question 64

What are three ways in which an electron can receive energy needed to move from ground state to excited state?

Answer 64

1. Atom in which electron orbits could be bombarded by high speed particles, such as electrons, and then emits light (in UV region) 2. Atom could absorb a photon of light (high frequency such as UV), and electrons can jump over intermediate energy states to reach higher energy states, and then when it loses energy it falls into one of intermediate states, emitting fluorescent light w/ wavelengths in visible light range 3. Atom could be subject to thermal agitation, when closely packed atoms subject to high temperatures electrons can transition to higher levels and to other atoms, producing incandescent light which exhibits continuous range of wavelengths

Question 65

What is the range of wavelengths of visible?

Answer 65

390 nm to 700 nm Shorter wavelengths correspond to violet light and longer wavelengths correspond to red light - just beyond visible spectrum on smaller wavelength side is UV light - just beyond visible spectrum on larger wavelength side is infrared

Question 66

Speed of light in a vacuum

Answer 66

c = E / B = 3 x 10^8 m/s

Question 67

Reflection

Answer 67

Wave is reflected when at boundary between media it bounces back to return into the medium from which it came Angle of incidence is equal to angle of reflection when light reflects off a plane (flat) surface

Question 68

Refraction

Answer 68

A wave is refracted when the wave bends as it continues on from one medium to the next Index of refraction (n) = c / v - ratio of speed of light in vacuum to speed of light in a particular medium, defines the amount that a wave refracts - All media have refractive indices greater than one - water has n = 1.3, glass has n = 1.5, and air has n = 1.0

Question 69

Snell’s Law

Answer 69

n1 sin \theta1 = n2 sin \theta2 Extent to which a change in speed will bend a light ray Theta1 is angle of incidence and theta2 is angle of refraction When light crosses into a new medium, frequency and phase remains the same while the wavelength and velocity change - If medium’s index of refraction is higher, wavelengths become shorter

Question 70

Total Internal Reflection

Answer 70

Light coming from a medium with higher index of refraction, angle of incidence can be so great as to cause total internal reflection, where photons will be reflected at angle of reflection and none will refract (critical angle) - Can derive following equation by setting angle of refraction to 90 deg, sin 90 deg = 1 Theta_critical = sin ^-1 (n2 / n1)

Question 71

Dispersion

Answer 71

Separation of light into different frequencies due to their different indices of refraction in a medium - Speed of light in medium depends on extent to which it is absorbed and re-emitted by medium - light more frequently absorbed and re-emitted travels more slowly - Most objects are more likely to absorb higher-frequency light than lower-frequency light, so blue light travels more slowly than red light and thus is bent more than red light Chromatic dispersion: white light is split by a prism in this phenomenon

Question 72

Thin film interference maxima and minima

Answer 72

Maxima: 2L = (m + 1/2) lambda / n2 for m = 0, 1, 2... Minima: 2L = (m) lambda / n2, for m = 0, 1, 2... Thin film interference results from some photons refracting and then reflecting off of thin layer to interfere constructively or destructively with other incident photons

Question 73

What causes thin film interference?

Answer 73

1. Phase changes associated with reflections off media that are more dense 2. Path length differences 3. Wavelength changes associated with changes in media

Question 74

Diffraction

Answer 74

Spreading of light that occurs when a wave bends around the edges of an object or opening All types of waves diffract and waves diffract around all objects - extent depends on size of object or opening relative to wavelength of wave - significant diffraction occurs when size of object or opening is on order of wavelength or smaller - smaller we make circle to focus light, the larger the spread of the light, must use electron beams with smaller wavelengths

Question 75

Young’s double-slit experiment

Answer 75

Light is projected onto a screen with two small slits, light is monochromatic and coherent (able to be forced into a parallel beam that spreads and weakens very little over great distances) - Light waves diffracting through two slits interfere with one another and produce predictable pattern of alternating light (path length different of lambda) and dark (path length difference of lambda /2 ) bands on detector screen - Waves from each slit start out in phase, but travel different path lengths to meet on detector - Distance between slits and screen so much greater than distance between slits, so paths of waves considered approximately parallel and difference in path length \delta considered equal to d sin \theta

Question 76

Maxima and minima in two-slit experiment

Answer 76

D sin \theta = m lambda, for m = 1, 2, 3, ... MAXIMA | D sin \theta = (m + 1/2) lambda, for m = 1, 2, 3, ... MINIMA

Question 77

Diffraction grating

Answer 77

Series of many small slits that diffracts a light source into component colors Slits are called rulings - grating may contain as many as several thousand rulings / mm - For each maximum, other than zeroth order, component parts of light source are spread out in spectra from shorter wavelengths (violet) to longer wavelengths (red) - Higher order maxima exhibit wider spread Formula the same as double-slit experiment

Question 78

X-ray diffraction

Answer 78

Atom spacing in crystals is exactly spaced roughly correct distance apart to act as a natural diffraction grating for x-rays X-rays that are projected at a crystal scatter and create regular interference patterns unique to structure of crystal Visualized as rays reflecting off distinct surfaces created within crystal Bragg’s law: 2 sin \theta = m lambda, d is distance between reflecting planes, theta is angle from relfective plane to ray

Question 79

Which lens and mirrors are converging?

Answer 79

A convex lens which is thicker in the center is converging, and will form either a real or virtual image - Forms a real, inverted image on the same side as the observer if the object is outside of the focal length - Forms a virtual, upright image on opposite side of observer if object is inside focal length A concave mirror converges light to the same side as the observer (forms a real inverted image)

Question 80

Which lens’ and mirrors are diverging?

Answer 80

A concave lens is diverging: - Forms a virtual, upright image on the opposite side of the observer A convex mirror is diverging: - Forms a virtual, upright image on the opposite side of the observer

Question 81

When is the focal distance negative? When is it positive? | When is the object distance negative? Positive?

Answer 81

Focal distance is negative for diverging mirror or lens Focal distance is positive for converging mirror or lens Object distances are negative when object is opposite side for mirror and when object is same side for a lens Object distances are positive when object is on the same side for a mirror and when object is the opposite side for a lens

Question 82

What is the sign convention for images?

Answer 82

Remember that real images are positive (converging) and virtual images are always negative (diverging)

Question 83

How do you calculate magnification for a mirror or lens?

Answer 83

m = - di/do = hi / ho | Where di is image distance (q) and do is object distance (p)

Question 84

What is the focal distance equation?

Answer 84

1 / f = 1/do + 1/di Remember sign conventions for object, image, and focal length! Remember that conventions for f and di are the same

Question 85

Lens aberrations

Answer 85

Images are often blurred and exhibit departures from theoretical images Chromatic aberrations: light of higher frequencies focuses closer to a lens than does light of lower frequencies - Higher frequency light is bent more than lower frequency light, meaning violet light focuses closer to lens than red light - Can be reduced by combining a converging lens of one index of refraction with a diverging lens of another index of refraction - Only seen with polychromatic light is used Spherical aberrations: rays farther from the center of a lens focus at different points than do rays closer to center of lens - Images are clear only when viewed through center of lens - Reduce by allowing light rays to pass only through the central portion of the lens

Question 86

Multiple lens systems

Answer 86

Use image of first mirror or lens as object of second mirror or lens and deal with each one at a time lateral magnification for two lens system: M = m1 m2 Effective power: Peff = P1 + P2 Appear in the context of optical instruments: manipulate properties of light to produce viewable images ( compound microscopes, refracting telescopes)

Question 87

Objective or eyepiece lenses

Answer 87

Two converging lenses used in microscope or telescope - Light from an object placed outside the focal point first encounters the objective, which forms a real, inverted image that acts as the object for the eyepiece - Eyepiece then forms an enlarged image that can be seen by observer (virtual, upright image since the image formed by objective falls inside focal length of eyepiece) - Object still ends up “where it belongs” on opposite side of lens and is inverted

Question 88

How does the eye focus light?

Answer 88

The cornea does most of the bending of the light, bending incoming light rays in general direction of the retina The incoming light then passes through the aqueous humor, through the pupil and then onto the crystalline lens, which is responsible for fine control necessary to precisely focus light on retina - Ciliary muscles contract to bend lens and focus on near objects and then relax to flatten lens and focus on far objects, adjusting the focal length in both cases

Question 89

Near-sighted vs. Far-sighted

Answer 89

Near-sighted (myopia): person can see objects clearly but has difficulty seeing far objects - Particularly good at bending light, since light that reflects off of nearby object will approach eye at sharp angle and must be bent significantly to focus on retina - Can be corrected with a diverging lens Far-sighted (hyperopia): person can see far objects clearly, but lens is not very good at bending light to focus on near objects - Can be corrected by converging lens Near point: closest distance at which eye can see object clearly Far point: farthest distance at which eye can see object clearly - normal vision person considered to have far point at infinity - Near point tends to increase with age as lens stiffens and resists bulging necessary to reduce focal length

Question 90

How do focal lengths of eyeglasses and contact lenses differ?

Answer 90

Eyeglasses sit on bridge of the nose about 2cm from cornea | Contact lenses sit on outer surface of the eye, closer to retina, so have smaller focal length