Physics 6C concepts

If an object is outside the center of curvature of a concave mirror

its image will be inverted, smaller, and real

Electric Flux

measure of the electric field that passes through a given area - mathematically, this equation says that electric flux is the integral of the electric field over the area of the surface, which is equal to the enclosed charge, divided by the permittivity of free space - permittivity of free space is a constant that relates electric charge to the physical effect of electric fields (Eo) - if the electric field is constant over the surface, then the left side of the equation become E times A--> EA=(q/Eo)

near point

normal is about 25cm closet distance at which eye can focus clearly

compound microscope magnification

M= M(eyepiece)m(object) = (Nl)/(fefo)

diverging lens

rays diverge from focal point

Wave theory of light is strengthened by

the interference and diffraction of light

AM signal

using the signal to modify the amplitude of the carrier

FM signal

using the signal to modify the frequency of the carrier

Virtual Image

what you see when you look into a plane (flat) mirror is an image which appears to be BEHIND the mirror (distance of image is negative)

Thin lenses

whose thickness is small compared to their radius of curvature - may be either converging or diverging

If the eye is focused at the near point:

M= (N/f)+1

B and E and velocity relationship

(E/B)=v here, v is the velocity of the wave: (speed of each wave0 v=c=1/(sqrt(eo(uo))

power is given in diopters (m-1)

P= (1/f)

f-stop

camera focuses image on film or electronic sensor; lens can be moved and size of opening adjusted (f-stop) Human eye also makes adjustments, by changing shape of lens and size of pupil - nearsighted eye is corrected by diverging lens - farsighted eye is correcred by converging lens

distortion

causes by a variation in magnification with distance from the lens

circular antenna

have a current induced by the changing magnetic flux

the power of a lens

is the inverse of its focal length - it s positive if it is converging and negative if its diverging

the height of the image of thin lens is

positive if the image is upright and negative otherwise

The focal length is ____ for converging lenses and ____ for diverging (for thin lens)

positive, negative

magnification

ratio of image height to object height - the negative sign indicates that the image is inverted. This image is between the center of curvature and the focal point, and this image is larger, inverted, and real

law of reflection:

the angle of reflection (that the ray makes with the normal to the surface) EQUALS the angle if incidence

astronomical telescopes

they need to gather as much light as possible, meaning that the objective must be as large as possible. Hence, mirrors are used instead of lenses, as they can be made much larger and with more precision

there is a certain range of distances over which objects will be in focus

this is called depth of the field of the lens- objects closer or farther will be blurred

Lensmaker's equation

this useful equation relates the radii of the curvature of the two lens surfaces, and the index of refraction , to the focal length

plane waves

waves from a far source

diffuse reflection

when light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies

focal point

where the rays converge

Ray tracing for thin lenses is similar to mirrors

1) rays come in parallel to the axis and exits through the focal point 2) this ray comes in through the focal point and exits parallel to the axis 3) this ray goes through the center of the lens and is undeflected

displacement current

change in the capacitor's charge over time Displacement current= (permittivity of free space)(change in electric flux over change in time) Id= (Eo)(change in E)/(change int t)

maxwell's equations

complete set of equations that describe electric and magnetic fields

refracting telescope

consists of two lenses at opposite ends of a long tube. the objective lens is closest to the object, and the eyepiece is closest to the eye M= (angle '/ angle)= (h/fe)/(h/fe)= -(fo)/(fe) (telescope)

Farsightedness can be corrected with a

convex diverging lens

nearsightedness

far point is too close (diverging lens)

Snell's law

refraction is what makes objects half-submerged in water look odd - light changes in direction when crossing a boundary from one medium to another- this is called refraction and the angle the outgoing ray makes with the normal is called the angle of refraction

For a convex mirror

the image is ALWAYS virtual, upright, and smaller

For a diverging lens

the image is upright and virtual

for a diverging lens

the image is upright and virtual

if light is a wave, there should be an interference pattern

the interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot)

from a concave spherical interface

the rays will diverge from a virtual image

Light very often travels in straight lines

we represent light using rays which are straight emanating from an object- this is called idealization, but is very useful for geometric optics

Formation of Images o=by spherical mirrors

- fro mirrors, we use three key rays, all of which begin on the object: 1) a ray parallel to the axis; after reflection it passes through the focal point 2) a ray through the focal point; after reflection it is parallel to the axis 3) a ray perpendicular to the mirror; it reflects back on itself - the intersection of these three rays gives the position of the image of that point on the object

Poynting vector (vector of Intensity)

- the energy transported by a wave per unit time, per unit area) called Intensity: S= (1/A)(dU/dt)= EocE^2 It vector form is shown on the picture - u can replace energy delivered= the energy density times the volume of space in which the energy is transported over a period of time AND then replace energy density with one of the energy density equations so the volume of space encompassed by the wave is equal to the unit area times the distance traveled--. after canceling out terms and such you get the final equation for intensity which is listed above

Electromagnetic wave of wavelength (lambda) and frequency (f) The electric and magnetic fields are given by

E=Ey=Eosin(kx-wt) B=Bz=Bosin *kx-wt) where k=2pi/lambda w=2(pi)f f(lambda)=w/k=v

Average value of S

S= (Erms)(Brms)/ u0

optic fibers

depend on total internal reflection; they are therefore able to transmit light signals with very small losses

Oscillating charges will produce

electromagnetic waves

Huygens' principle

every point on a wave front acts as a point source; the wave front as it develops is tangent to all wavelets - principle is consistent with diffraction

If the eye is relaxed (N is the near point distance and f the focal length):

eye focuses at infinity N=25 cm for normal eye M= (angle '/ angle)= (h/f)/(h/N)== N/f

Maxwell's third equation (Faraday's Law)

faraday's law of induction - tells us that a changing magnetic field will induce an electric field

far point

farthest distance at which object can be seen clearly. normal is at infinity

internal reflection

if the angle of incidence is larger than the critical angle - binoculars often use total internal reflection; this gives true 100% reflection, which even the best mirrors cannot do

Energy is stored in both electric and magnetic fields. giving the total energy density of an electromagnetic wave:

U (total energy per unit volume within the wave overall)= Ue+ UB= (1/2)eoE^2 + (1/2) B^2/ uo since Ue= (1/2) Eo(E^2) and Ub= (1/2)(B^2/ uo) Each field contributes half the total energy density which is the amount of energy stored in a field per unit volume u= Eo (E^2)

if a changing electric field is generated, then a magnetic field is induces, which results in

a changing magnetic field that induces an electric field, and the cycle continues - this is what produces the oscillations in em waves

diverging lens focal point

a diverging lens (thicker at the edge than in the center) makes parallel light diverge; the focal point is that point where the diverging rays would converge if projected back

Maxwell's fourth equation (Ampere's Law)

a more general form of Ameperes law- tells us that a magnetic field is produced by a current or by a changing electric field

A similar effect as thin films takes place when

a shallowly curved piece of glass is placed on a flat one. When viewed from above, concentric circles appear that are called Newton's rings

Interference in thin films

another way path lengths can differ, can waves interfere, is if they travel through different media. If there is a very thin film of material- a few wavelengths thick- the light will reflect from both the bottom and the top layer causing interference.

The frequency of an em wave is related to its wavelength and to the speed of light

c=(lambda)f

near fields

close to the antenna the fields are complicated and are called

Nearsightedness can be corrected with a

concave diverging lens (pushes the focal point farther so that it hit the back of the eye since normally the focal point is before)

A refracting telescope

consists of two lenses at opposite ends of a long tube. The objective lens is closest to the object, and the eyepiece is closest to the eye

focal length

half the radius of curvature f= (r/2) Distance from the center of a lens or mirror to the focal point

straight antenna

have a current induced in it by the varying electric fields of a radio wave

Radiation Pressure

in addition to carrying energy, electromagnetic waves also carry momentum This means that a force will be exerted by the wave - The radiation pressure is related to the average intensity. It is a minimum if the wave is fully absorbed: P=(F/A)=(1/A)(dp/dt)= (1/(AC))(dU/dt)= S/c and a maximum if it is fully relflected: P= 2S/(c)

combo of lenses

in lens combos, the image formed by the first lens becomes the object for the second lens (this is where object distances may be negative) The total magnification is the product of the magnification of each lens

The combination of lenses

in the lens combo, the image formed by the first lens becomes the object for the second lens (this is where object distances may be negative). The total magnification is the product of the magnification of each lens

chromatic aberration

light of different wavelengths has different indices of refraction and focuses at different points

critical angle

light passes into a medium with a smaller index of refraction, the index of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90 degrees, this is called the critical angle sin (theta c)= (n2/n1)sin 90= (n2/n1)

index of refraction

light slows somewhat when traveling through a medium. the index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium: n=(c/v)

Electric and magnetic waves are _____ to each other and to the _____________

perpendicular, direction of propagation

Converging lens

rays converge at focal point

spherical aberration

rays far from the lens axis do not focus at the focal point

refraction at a spherical surface

rays from a single point will be focuses by a convex spherical interface with a medium of larger index of refraction to a single point, as long as the angles are not too large

Gauss's law

relates the electric field on a closed surface to the net charge enclosed by that surface. The analogous law for magnetic fields is different, as there are no single magnetic point charges (monopoles)

Ampère's law

relates the magnetic field around a current to the current through a surface - in order for law to hold, it can't matter which surface we choose -- the creation of a magnetic field by a changing electrical field- between the plates of the capacitor

maginifying glass

simple magnifier a converging lens - allows us to focus on objects closer than the near point, so that they make larger, and therefore clearer, image on the retina

If the curvature is small

the focus is much more precise; radius of curvature r

dispersion

the spreading of light into the full spectrum is called dispersion

Solution

achromatic doublet, made of lenses of two different material

compound microscope

also has an objective and an eyepiece; it is different from a telescope in that the object is placed very close to the eyepiece

Rays coming from a faraway object

are effectively parallel

Spherical mirror

are shaped like sections of a sphere, and may be reflective on either the inside (concave) or outside (convex) - parallel rays striking a spherical mirror do not at all converge at exactly the same place if the curvature of the mirror is large; this is called spherical aberration

solutions

compound-lens systems; use only central part of lens

We can use geometry to find conditions for constructive and destructive interference

dsin(theta)= m(lambda) m=0,1,2.. (constructive) and dsin(theta)= (m+0.5)(lambda) m=0,1,2.. (destructive)

Maxwell's second equation (Gauss's Law)

integral will always equal zero for a closed surface--> magnetic flux always zero since magnetic sources are always dipoles and magnetic field lines that leave from north pole return back to the south pole - magnetic field lines form a continuous loop- have no beginning and no end

farsightedness

near point is too far away

Maxwell's First Equation (Gauss's Law)

the electric flux through a closed surface is proportional to the total charge enclosed by that surface (surface is anything that encloses the charge)

two sources of light are coherent if

they have the same frequency and maintain the same phase relationship

Distance of object, image and focal length relationship

(1/d object)+ (1/ d image)= (1/ focal length)

Problem solving: Interference

1) interference occurs when two or more waves arrive simultaneously at the same point in space 2) constructive interference occurs when waves are in phase 3) destructive interference occurs when the waves are out of phase 4) an extra half-wavelength shift occurs when light reflects from a medium with higher index of refraction

Huygens' principle can also explain the law of refraction.

As the wavelets propagate from each point, they propagate more slowly in the medium of higher index of refraction. This leads to a bend in the wave front and therefore in the ray - pi shift!! The frequency of the light does not change, but the wavelength does as it travels into a new medium: wavelength n= wavelength in vacuum/ n

The electric fields at the point P from the two slits given by

E1= E10(sin angularfrequencyw+ (2(pi)/(lambda))dsin(theta) see lecture 04/19 week three if confused

The time-averaged intensity is proportional to the square of the field

I=(Iinitial)(cos(d*pi*y/(lambda* l))^2

The power of a magnifying glass is described by its angular magnification:

M= (angle '/ angle)

magnification of a telescope

M= (new angle)/ (original angle)= (h/fe)/(h/fo)= -(fo/fe)

Camera adjustments:

Shutter speed: controls the amount of time light enters the camera. A faster shutter speed makes a sharper picture. • f-stop: controls the maximum opening of the shutter. This allows the right amount of light to enter to properly expose the film, and must be adjusted for external light conditions. • Focusing: this adjusts the position of the lens so that the image is positioned on the film.

The object distance is positive when the object is on the same side as the light entering the lens; other wise its negative (for thin lens)

The image distance is positive if the image is on the opposite side from the light entering the lens; other wise its negative

A beam of light reflected by a material with index of refraction greater than that of the material in which it is traveling, changes phase by

180 degrees 1/2 cycle

The sign conventions are slightly different: for thin lens as compared to mirrors

1.The focal length is positive for converging lenses and negative for diverging. 2.The object distance is positive when the object is on the same side as the light entering the lens (not an issue except in compound systems); otherwise it is negative. 3.The image distance is positive if the image is on the opposite side from the light entering the lens; otherwise it is negative. 4.The height of the image is positive if the image is upright and negative otherwise