UWorld Light and Sound

Cornea and Lens

Optical components of the eye that form converging lens which focus light on the retina (film of a camera).

Refractive Errors

When the eye is unable to focus light rays on the retina.

Hyperopia

Farsightedness, a condition that results when the optical power of the eye (S = 1/f) is insufficient to refract light rays from nearby objects.

Hyperopia is corrected by:

Placing a converging lens in front of the eye with a optical power system with a greater optical power. This shifts the focal length towards the eye’s lens and light from nearby objects is focused on the retina.

Myopia

Nearsightedness, describes a visual condition in which the eye forms an image of distant objects at a focal point in front of the retina. Correcting myopia shifts the image away from the lens.

Spherical Aberration

The optical deficiencies of lenses with perfectly spherical surfaces. The surfaces of the cornea or lens are not perfectly spherical so there is no spherical aberration.

Refraction

The bending of light that takes place as light traveling at an angle passes from one medium to the next. Light will refract/bend toward or away the normal (an axis perpendicular to the interface between media) depending on the index of refraction (n) of each medium.

Snell’s Law

n1 sin theta 1 = n2 sin theta 2

theta 1 = angle of incidence (the angle at which light approaches/enters)

theta 2 = the angle light departs/exits the interface between media

n1 / n2 = sin theta 2 / sin theta 1

Angle of Refraction will decrease:

When angle of incidence increases

Total Internal Reflection

Only occurs when light leaves a medium with higher refractive index and enters a medium with lower refractive index

Energy of Light Equation

Energy of Light = (h)(f)

h = planck’s constant f = frequency

Converging/Convex Lens

Converges parallel rays of light toward its focal point. A real image is formed from the convergence of the refracted light rays on the side of the lens opposite of the object. Real images are always inverted. (CRII “cry” convergence, real images, inverted)

Diverging/Convex Lens

Spreads parallel rays of light away from a focal point. A virtual image is formed from the apparent convergence of refracted light rays traced back to the same side of the lens as the object. DIV (diverging, virtual image) virtual images are upright. Image is virtual because it isnt actually converged.

Myopia is corrected by:

Diverging Lens

Hyperopia is corrected by:

Converging Lens

Dispersion

Light separating into its colors. Different frequencies of color have different refractive indices in the same medium and angle of refraction is different for different colors of light.

Chromatic Aberration

Formation of blurry images due to effects of dispersion through a lens.

Refractive Index of Light increases with:

Frequency and has a higher index of refraction/refracts more

Index of Refraction (n)

n = speed of light in a vaccuum c / speed of light in a medium v

If index of refraction is higher in the second medium, light rays refract toward the normal and if index of refraction is lower it refracts away from the normal.

Incident Ray in Air (Snell’s Law)

n = 1

Thin Lens Equation

S = 1/o + 1/i

S = Len’s strength (1/f) , closer the image is focused to the lens the greater the lens strength.

o = object lens to camera, i = image lens to retina, measured in units of diopters (D) (inverse meters)

1 / 0.5 + 1 / 0.025 = 2 + 40

Thin Lens Equation 2

1/f = 1/o + 1/i

The ratio of the image height to the object height is equal to the ratio of their respective distances. The ratio of the image’s distance to the object’s distance is equal to the ratio of the image’s height to the object’s height (1:1)

Lens Strength

Measured in Diopters (inverse meter m -1)

S = 1/f ( S - lens strength and f = focal point)

2 cm = 0.02m = 50 D

S = S1 + S2…. S = other diopters

The values is positive for converging lens and negative for diverging lens

Total Distance Equation

d(T) = ct(E)

d(T) = distance time

c = speed of sound

t(E) = echo time

d1 = d(t) / 2

d2 = ct(E)

Tm = d2 - d1 Distance from one point to the other point

Spherical Aberration Occurs:

when lenses with perfectly rounded surfaces focuses on light at multiple focal points. spherical aberration is most pronounced among light rays entering and exiting the periphery of converging lens.

The combined lens strength of a two lens system equals:

the sum of the strengths of each lens

S = S1 + S2

Overall lens strength = strength of first and second lens

Ultrasonic/Ultrasound Wave

Mechanical waves that propagate at a frequency above the human auditory spectrum (20 Hz). Operate like sound waves that can be detected by human ear. The small wavelength allows them to propagate throughout the body without diffracting significantly

Shock Wave Ultrasound

Use high frequency waves to cause destructive , high amplitude vibrations within target structures. Frequency of shock waves should match the resonance frequency of the target structure.

f = f0 high amplitude vibrations can occur

f does not = f0 high amplitude vibrations cannot occur

f = shock wave frequency f0 = resonance frequency

Attnenuation

All sound waves attenuate when propagating through a medium. May occur as sound waves pass through media.

Doppler Ultrasound

Imaging technique that allows for the characterization of dynamic structures.

Sound

Sound propagates through vibrations of molecules as longitudinal pressure waves and therefore cannot exist as a vacuum. The attenuation of sound is greatest in soft materials and increases with distance. Sound travels slowest in gas and fastest in solids.

Intensity Equation

Power / Area

Decibel Scale

[DB] = 10 log (I/I,s)

I = Intensity and I,s = Source Intensity

The decibel scale (DB) is logarithmic and relates the perceived loudness of sound to its actual intensity. For each 10 fold decrease, sound intensity decreases by 10 DB. A 100 fold decrease in sound intensity corresponds to a decrease by 20 DBs.

Doppler Effect (delta f)

When the observed frequency and wavelength of a sound are shifted from those of the original due to relative motion between the source and the observer.The frequency shift is positive when the source velocity is negative (moving closer) and negative when the source velocity is positive (moving away)

Sound is propagated in the form of:

longitudinal waves of oscillating pressure. Compressions (areas of high pressure) and rarefractions (areas of low pressure) are formed through vibrations of the molecule through the medium.

The rapid expansion and contraction of crystals creates:

pressure waves (sound) by vibrating nearby particles

Period

T of a wave, the amount of time for one cycle/wavelength to pass through a fixed point.

T = 1/f

f = frequency

Doppler Effect Equation

delta f / f = v / c

delta f = frequency shift, f = original frequency, v = velocity between source and observer, c = speed of wave in medium

Speed of Light c

3 × 10^8

Photoelectric Effect

The ejection of electrons from a surface due to the absorption of electromagnetic radiation. Although higher intensity electromagnetic radiation exhibits greater electric field oscillators some do not cause ejections of electrons ever because of electric potential energy between positive and negative charges.

hf = ½ mv² + W

W = work function

1/2mv² = kinetic energy of electron

hf = energy of light

Electromagnetic Equation

E = hf

h = planck’s constant = 6.6 × 10^-34

f = frequency

The magnitude of energy absorbed through electromagnetic radiation must exceed W (Work Function = the electric potential of an elelctron)

Antinodes

Exists at locations of maximal wave amplitude (where lines are spaced out)

Nodes

Exists at locations of zero amplitude (where lines meet)

Velocity of a Wave Equation

v = (wavelength)(frequency)

Source Frequency Equation

source frequency = c (speed of light 3 × 10^8 ) / wavelength

If observed frequency = source frequency there is:

no frequency shift (Doppler Effect delta f)

On a displacement vs time graph:

instantaneous velocity is the slope of the graph.

If it is a straight line/not moving their is no velocity (v = 0) and if there is a slope or incline v is - or +

All waves are characterized by:

wavelength, frequency, and amplitude

Mechanical Waves

Mechanical waves propagate through a medium. Wavelength and amplitude depend on the type of medium but frequency is independent of the medium

Energy of a Photon

E = hf

h = plank’s constant , f = frequency

when dividing by a negative exponent add the exponent ^5 / -^15 = ^ 20

Photon Speed

c = (wavelength)(frequency)

c = 3 × 10^8

so E can be E = hc / (wavelength)

Intensity

Intensity = Power / Area (Power = Energy / Time)

Higher energy and higher rate = higher intensity

Light (Speed)

Light travels fastest in a vacuum

Index of Refraction Equation

n = c / v

n = index of refraction

c = speed of light in. vacuum

v = speed /velocity of light in a material

Energy of a photon

E = hf

h = plank’s constant and f = frequency

A photon’s frequency will decrease as its energy decreases because they are proportional. The velocity of a photon is independent of the photon energy

Visible Light Spectrum

The part of the electromagnetic radiation spectrum that the human eye can detect, Visible light has a wavelength of 400 to 750.

Wavelength can be measured:

Using the distance between adjacent crest or through points or intersecting point of a wave through the x axis to the other intersecting point of a wave through the x axis.

Standing Waves

Stationary waves that can be produced with strings, pipes, and other common objects. Perturbing a string fixed at both ends produces multiple standing waves (numbered n = 1, 2, 3) known as harmonics.

Fundamental Frequency (f, 1)

The frequency of the first harmonic (n = 1) and is the lowest frequency standing wave that can be produced within an object.

f(1) = v / wavelength 1

f(1) = fundamental frequency

v = velocity

Fundamental frequency is proportional to speed and inverse to wavelength.

Wavelength of each harmonic in a string fixed at both ends is:

proportional to the string length (L)

wavelength(n) = 2L / n (n = harmonic)

f = v / wavelength

v = velocity L = length

For string fixed at both ends, the wavelength of each harmonic is proportional to the string length

Bulk Modulus (B)

Refers to the compresiblilty of a substance. In combination with density (d), bulk modulus influences the velocity of sound waves through fluids (the atmosphere). Unrelated to standing waves.

When the properties of the medium are independent of wavelength:

waves travel with a speed v

v = (wavelength)(frequency)

Wave Speed

Wave speed is independent of frequency and depends only on the properties of the medium of propagation. Changing the medium changes the speed of the sound in the medium.

Magnification

The ability of lenses to produce images that are smaller or larger than a real image.

M = h(i) / h(o)

h(i) = image height, h(o) = object height

Mulitiple Lens Placed in Series Equation

M tot = M1 x M2 x M3. . .

Speed of Light Equation c

c = (wavelength)(frequency)

c = speed of light

X-Rays

X-rays are electromagnetic radiation and have a speed in a vacuum equal to the speed of light, independent of the. wavelength of the x rays

Refractive Index Equation

n = c / v

n = refractive index, c = speed of light, v = speed in the medium

Electric Field

E = F / q

E = Electric Field

q = charge

F = Electrostatic Force

Electric Field Lines

Denote the direction and relative strength of a field. Field lines point toward the lowest voltage in the field and away from the highest voltage in the field.

Electrical Conductors

Allow the flow of electric charges when they are exposed to a voltage.

Electrical Insulators

Do not contain mobile charge carriers and do not allow electric charges to flow when voltage is exposed.

A vacuum is an:

electric insulator because it does not contain charge carriers

X-Ray Image Intensifier

Performs a series of conversion and amplification steps. Determining the efficiency of one particular steps requires measurements of the input and output for that individual step.

Conservation of Charge

E = PE + KE = constant

PE (electron) = qV

KE = ½ mv²

KE = kinetic energy and PE = potential energy q = charge V = voltage

wave speed equation

wave speed = (frequency)(wavelength)

wavelength of standing wave (n) = 2L / n

L = length and n = number of antinodes

Intensity Equations

Intensity = Energy / (Area)(Time)

Intensity = Power / Area = P / pi r²

Standing Waves

On a cord are generated due to interference between incident waves and reflected waves, which moves in opposite directions along the cord. The standing waves create nodes (points of zero amplitude) and antinodes (points of maximal amplitude). At the fundamental resonance there is one antinode so:

(wavelength standing wave) = 2L

f = v / wavelength = v / wL

speed of wave (v) is proportional to sqrt(T) (tension)

Energy E of Mechanical Waves

Energy carried by a mechanical wave depends on its amplitude. E is proportional to A². Mechanical waves with a higher amplitude carry higher energy than those with lower amplitude.

Retina

Light entering the eye is refracted by the lens to form an image on the retina.

Myopia (Nearsightedness)

Lens of the eye bends the light too much, forming the image in front of the retina. It is corrected using a concave/diverging lens.

Lens Strength (S)

S is equal to the inverse of the focal length of the lens. S = 1 / f

The thin lens equation is used to calculate S: S = 1/o + 1/i

The units for S are Diopters (D) which are equivalent to m^-1

Specific Gravity

SG = density of object / density of water

SG = (d object)(g)(V) = (Weight) / (d water)(g)(V) = (Buoyant Force)

SG = Weight of object / Buoyant Force

Fluid Barometer

Can be used to measure pressure such as atmospheric pressure. The hydrostatic in the barometer’s fluid filled column is equal to the applied pressure.

P = Hydrostatic Pressure

Hydrostatic Pressure

P(h) = dgh

d= density

g = gravity

h = height

Diffraction

The bending of light around edges or objects. Light passing through a single slit forms a diffraction pattern of alternating dark and bright bands when the width of the slit is comparable to the wavelength. The waves of light exiting the slit travel at different based on their original position within the slit. When the distance traveled by two light waves differs by one half of wavelength, the waves are 18- degrees out of phase and cause destructive interference, forming a dark band. A difference in distance travelled equal to an integer multiple m of wavelength results in constructive interference and forms a bright band.

Angle of Dark Bands EquationS

Sin theta = (integer)(Wavelength) / width of slit

Period Equarion

T = 1 / f

remember 500 × 10^12 = 5 × 10^14 and dividing 5 × 10^14 = 5 × 10^-14

Sound waves travel fasteer:

in the warm air and slower in the co

Intensity Equation

I = Power / Area = P / pi r² (Area decreases exponetionally when intensity increases)

Resonates

Generating standing waves on a string fixed at both ends due to interference between incident waves and reflected waves, which movies in opposite directions along the string.

Fundamental Resonance

There is one antinode (point of maximal amplitude) and the wavelength of the standing wave is twice the length of the string L

wavelength = 2L, wavelength = 2L / (n = harmonic), wavelength = v / f,

Fundamental Frequency = f(n) = n f(1), n = harmonic and f1 = fundamental resonance frequency

To count the harmonics count how many times the wave crosses the axis

Speed Wave Equation

v = sqrt(F/linear density), F = tension force

Frequency is proportional to sqrt(F/linear density)

For constant wavelength, an increasing the string tension also increases wave speed and frequency. High frequency results in crests that are closer together on a graph of displacement as a function of time.

Speed of Light. (C)

(speed of light) c = (wavelength)(frequency)

GHz

Giga Hz = 10^9

THz

Tera Hz = 10^12

Dividing by a Negative Exponenet:

Add the exponents

Ohm’s Law (Multiple Resistors)

V = IR(eq)

R(eq) = R1 + R2

Mechanical Power

P = W / t

W = Work, t = time

Work = (force)(distance) so P = F(d/t) = Fv

Friction decreases speed.

When sound reflects off an interface between two media:

The reflection has a reduced media because some of the sounds is transmitted into the new media. The speed, wavelength, and frequency of the reflection are the same as that of the original sound wave.

Energy Equation (Photon)

E = fh

h = Planck;s constant f = frequency