What is Light?

I.  Particle Theory

·      the early Greeks proposed light was a stream of particles (corpuscles) that were emitted by a light source and stimulated the sense of sight upon entering the eye

·      Newton supported this theory and used it to explain the laws of reflection and refraction

 

II.  Wave Theory

1678- Christian Huygens (Dutch)

Ø  used wave theory to explain reflection and refraction

 

wave theory was NOT accepted due to

Ø  lack of medium

Ø  why doesn’t light bend around corners?

Ø  Newton’s reputation

 

1801 – Thomas Young

Ø  showed light exhibits interference behavior

Ø  with 2 sources, light could combine to create constructive and destructive interference

 

1850 – Jean Foucalt

Ø  provided further evidence of the inadequacy of the particle theory by showing that the speed of light in liquids is less than in air

Ø  this contradicts the particle theory which proposed the speed of light would be higher in glass and liquids than air

 

1873 – James Clark Maxwell

Ø  predicted light was a form of high-frequency electromagnetic wave

Ø  predicted speed of about 3 x 108 m/s

 

1887 Heinrich Hertz

Ø  produced and detected EM waves

Ø  showed these EM waves exhibited reflection, refraction, and all other wave properties

Ø  also observed the photoelectric effect (the ejection of electrons from a metal whose surface is exposed to light)

Ø  this photoelectric effect could NOT be explained by using the wave theory

 

 

1905 Albert Einstein

Ø  used Max Planck’s idea of quantization to explain photoelectric effect

 

III.  Dual Nature of Light

In some cases light acts like a wave, and in other cases it acts like a particle. 

 

The Aether

·      If light behaves like a wave, then what does it travel through?  What is doing the waving??

·      Physicists proposed that there must be some mysterious material, called aether, surrounding and permeating everything, including space, to carry the light.

·      It had to be very light, very hard to compress, and allow solid bodies to pass through it freely without aether resistance or the planets would slow down.

 

How do we detect this aether??

 

Michelson – Morley 1887 (Nobel Prize 1907)

·      devised a clever experiment to attempt to detect this aether

·      after many attempts, no aether wind was detected

·      He was reluctant to give up the aether, because if there was no medium, what did light travel through?

 

Maxwell’s equations were the key

·      His work with EM waves predicted a definite speed for light, and this was what Michelson was getting. 

·      But what is the speed relative to if not the aether?

 

Emitter theory

·      light travels relative to the source of light – sort of like a gun on a tank

·      this theory was proven false in the 1960’s

 

Einstein

·      light is not like sound – with a definite speed relative to a medium

·      light is not like bullets – with a definite speed relative to a source

 

 

Theory of Special Relativity

The Laws of Physics are the same in any inertial frame, and in particular any measurement of the speed of light (or any EM wave) in any inertial frame will always give 186,300 miles per second.

 

This implies that there is no “at rest” state.  So then the aether cannot exist.

 

 

How was the speed of light determined?

 

I.  Galileo

Ø  proposed 2 observers stand in towers 5 mi apart with shuttered lanterns

Ø  the first person would shine the light, then the 2nd person would shine their light as soon as they saw the 1st light

Ø  inconclusive because the speed of light is too fast

 

II.  Ole Roemer – Danish astronomer 1675

Ø  observed Io – moon of Jupiter – T = 42.5 hr

Ø  T> avg T when Earth receded from Jupiter

Ø  T < avg T when Earth approached Jupiter

Ø  over a 3 month time interval, he correctly predicted that an eclipse would be 10min behind schedule

Ø  important because this showed that the speed of light was finite

Ø  Huygen used Roemer’s data to estimate a lower limit of 2.3 x 108 m/s

 

III.  Armand Fizeau/Jean Foucault – 1850 France

Ø  first successful terrestrial method

Ø  measure the time it takes light to travel from a source to a distant mirror and back    c = 2d/t

Ø  to measure the time, Fizeau used a rotating toothed wheel – which converts a beam into a series of light pulses

Ø  speed of wheels rotation effected what observer saw – might be blocked by a tooth

Ø  knowing d, angular velocity of the wheel, they found c

      c ≈ 3.1 x 108 m/s

Ø  Foucault’s method was similar, but used a rotating mirror instead of a toothed wheel.  At one point in the mirror’s rotation, the reflected beam fell on a distant mirror, which reflected it right back to the rotating mirror, which had turned through a small angle.  Knowing the speed of the rotating mirror, the position of the reflected beam and the amount the mirror had rotated, they also found c to with about 1000 miles per second.

 

IV.  Albert Michelson - 1879

Ø  duplicated Foucault’s method – but redesigned for greater accuracy

Ø  increased distance to 2000ft (instead of 60 ft)

Ø  invested in high quality lenses and mirrors

Ø  result was 186,355 miles per second

Ø  twenty times more accurate than Foucault

 

 

Section 14-1  Characteristics of Light

 

Electromagnetic wave – a transverse wave consisting of oscillating electric and magnetic fields at right angles to each other

 

white light can be separated into six elementary colors of the visible spectrum

      red, orange, yellow, green, blue, violet

 

the electromagnetic spectrum – consists of a range of different EM waves – distinguished by their wavelengths and frequencies

 

All EM waves move at the speed of light.

 

For our purposes,   c≈ 3.0 x 108m/s

 

      v = fλ         or         c = fλ

 

Huygens Principle (1678)

- a geometric construction for determining the position of a new wavefront at some instant from the knowledge of an earlier wavefront

- a wave front can be divided into point sources and the line tangent to the wavelets from these sources marks the wave fronts new position

 

Brightness decrease by the square of the distance from the source.  This is one more example of an inverse square relationship.

 

Section 14-2 Flat mirrors

 

reflection – the turning back of an EM wave at the surface of a substance

 

amount of the wave reflected depends on the surface

no surface is a perfect reflector

 

diffuse reflection – light reflected in many directions due to the “roughness” of the surface compared to the wavelength of the incoming light

 

specular reflection – light reflected in one direction

 

As measured from a line normal to the surface at the point of incident light, the angle of incidence is equal to the angle of reflection.

 

θi = θr

 

Flat Mirror characteristics – always produces an image that appears behind the mirror – cannot be displayed on a physical surface

virtual image – image formed by light rays that only appear to intersect

 

object distance = image distance

object height = image height

 

Use a ray diagram to predict image location

 

Ray 1.  Draw perpendicular to the surface and continue to draw through the mirror.

 

Ray 2.  Draw at any angle to the surface.  Draw the reflected ray and the same angle from the normal line, and continue to draw this back through the mirror.

 

Section 14-3  Curved Mirrors

 

concave spherical mirror - an inwardly curved, mirrored surface that is a portion of a sphere

 - it converges incoming light rays

 - it forms real images (they can be projected on a screen)

 

R – the radius of curvature of the mirror – the distance from the mirror’s surface to the center of the sphere

C – the center of the sphere of which the mirror is a part

F – the focal point of the mirror

f – the focal length

      * for a spherical mirror, f = ½ R

 

Mirror equation            1/p + 1/q = 2/R

                                    1/p + 1/q = 1/f

 

      1           +      1         =   1

object              image         focal

distance           distance     length

 

Mirror conventions:

·      front side of mirror – real images

·      back side of mirror – virtual images – light rays do not exist

·      drawn so that the front of the mirror is on the left of the surface

·      distances on the front side are positive

·      distances on the back side are negative

·      object and image heights are positive when above the principal axis

·      object and image heights are negative when below the principal axis

see table 14-4 p. 538

 

magnification – the measure of how large or small the image is with respect to the original object’s size

 

      M = h’/h = -q/p

 

      M = image height   = image distance

            object height     object distance

 

*if M<1 the image is smaller than the object

*if M>1 the image is larger than the object

Sign conventions for magnification

      upright       M is +         image is virtual

      inverted     M is -         image is real

 

How to draw reference rays for curved mirrors:

      (see table 14-3 p. 534)

 

Example:  When an object is placed 30.0 cm in front of a concave mirror, a real image is formed 60.0 cm from the mirror’s surface.  Find the focal length.

 

 

 

Example:  A square object is placed 15 cm in front of a concave mirror with a focal length of 25 cm.  A round object is placed 45 cm in front of the same mirror.  Find the image distance, magnification,  and type of image formed for each object.  Draw ray diagrams for each object to confirm your answer.

 

 

 

 

 

convex spherical mirror – an outwardly curved, mirrored surface that is a portion of a sphere

·      it diverges incoming light rays

·      reflected rays look as though they originated from some point behind the mirror

·      it has a negative focal length

·      the focal point and the center of the sphere are behind the mirror

·      magnification is always less than 1 (smaller)

 

example:  The radius of curvature of a convex mirror is 12.0 cm.  Where is the focal point located?

 

 

example:  Find the position of the image for an object placed at the following distances from the mirror in the previous question:

      p = 1 cm, 2 cm, 3cm, 6cm, 12 cm, 30 cm, 50 cm

 

How does the position of the image vary as the object moves farther away from the mirror?

spherical aberration – the blurred image produced by rays that are far from the principal axis in a spherical mirror

 

Parabolic mirrors –

·      concave

·      part of a paraboloid

·      they eliminate spherical aberration

·      all rays parallel to the principal axis converge at the focal point

·      a very clear real image is produced

·      used in a reflecting telescope

 

COLOR

-objects absorb certain wavelengths from light and reflect the rest

-color depends on which wavelengths of light shine on the object and which wavelengths are reflected

 

additive primary colors – red, green, blue light

-when added in varying proportions they can form all colors of the visible spectrum

subtractive primary colors – cyan, magenta, yellow pigments – filter out all light when combined

Additive color combinations (light)

 

red + blue = magenta          magenta + green = white

 

red + green = yellow           yellow + blue = white

 

blue + green = cyan            cyan + red = white

 

 

Subtractive color combinations (pigments)

 

magenta + cyan = blue        blue + yellow = black

 

magenta + yellow = red       red + cyan = black

 

cyan + yellow = green         green + magenta = black

 

 

linear polarization – the alignment of EM waves in such a way that the vibration of the electric fields in each of the waves are parallel to each other

 

similar to passing a waving rope through a picket fence

-good sunglasses are polarized to reduce road glare