Dispersion

1
Dispersion

• Dispersion the refractive index depends not only
  on the substance but also on the wavelength of
  the light, this dependence on wavelength is
  called dispersion
• Wave characteristics
• the frequency of the wave is constant transmit
  from one material to another
• the wavelength of the light changes due to

2
Change of wavelength

• the waves get squeezed from smaller refractive
  index material to greater one
• or stretched reversely

3
Dependence of n on wavelength

• The refractive index changes for different
  wavelengths
• Normally, for a certain medium, the value of n
  decreases with increasing wavelength

• violet shortest ? - deviated most, biggest n
  largely deviated
• red longest ? - smallest n less deviated
• other colours in the intermediate positions ?
  produce fan-shaped spectrum

4
Spreading of optical square pulses

• Laser (LED) generated pulses transit through
  optical fibre

5
Polarization

• A propagating light wave may be expressed
  uniquely in terms of its E-vector
• Most sources of light will be composed of many
  waves and their E- vectors randomly orientated
  with each other.
• - Beam is unpolarised or randomly polarised
• In some cases waves are constrained to oscillate
  in preferential planes - Beam is polarised

6
Brewsters law polarization by reflection
Randomly polarized plane light

• Normally the electric-field vector perpendicular
  to the plane of incidence are reflected strongly
  than others lie in this plan
• But at one particular angle of incidence, the
  electric-field lie in this plane is not reflected
  at all but refracted completely - polarizing
  angle ?P
• The incident light hits interface at angle larger
  than polarizing angle, the reflected light is
  completely polarized perpendicular to the
  incident plane

7
Brewsters law polarization by reflection
At polarizing angle, it was observed the
reflected ray is normal to the refracted ray -
Brewsters law
nasin?pnbsin?b nbsin(90-?p) nbcos?b
8
Huygens law

• Huygens principle - geometrical method to find
  wave front
• Every point of a wave front may be considered the
  source of secondary wavelets that spread out in
  all directions with a speed equal to the speed of
  propagation of the wave

• Christian Huygens stated in 1678
• Used to derive the laws of reflection and
  refraction

9
Wave front of point source

• Point source
• Spherical wave front AA
• Wave front after time of t?
• Each point as a point source and generate
  spherical wavelets with radius of ?t
• Envelope of the series wavelets constructs new
  wave front BB

10
Derive law of reflection

• Considering a plane wave approaching a reflecting
  surface MM'with wave front AA? travelling speed
  ?
• After a time interval of t, the successive wave
  front can be derived by wavelets
• For the portion doesnt reach the surface, the
  wavelets spread out unhindered and the envelope
  gives new wave front of BO
• For the portion reaches surface, the wavelets
  travel direction is changed by the surface, the
  envelope of all the reflected wavelets gives new
  wave front of OB

11
Law of reflection
M'
B

• Consider triangles of A'O'O and A'PO, they are
  congruent
• Right triangles
• Common side of AO
• OPAOvt
• Then ?i ?r

O
A
?i
?r
B'
P
?i
O
A'
?r
M
12
Derive of Snells law

• After a time interval of t
• The wave front envelope formed by the wavelets
  dont hit transmitted surface is OB with distance
  of vat
• the wavelet hits point A travels to point B
  with distance of vbt

13
Derive of Snells law

• From triangles OOA OBA

? Snells law
14
Geometrical Optics to understand study image
by ray model

• Using ray model, simple geometry trigonometry
  to study mages formed by mirrors, refracting
  surfaces thin lenses
• understand familiar optical instruments camera,
  microscopy telescopes

15
Image formed by a plane mirror

• Ray AB is reflected ack
• Ray AC is reflected to CD
• Intersect of extended rays AB and DC is the image
  of point A
• Same to the point O, the image is O'
• The image of subject OA is O' A'
• the image formed by plane mirror is erect, height
  has same sign

lateral magnification
16
Sign rules

• Object distance ? is positive when the object is
  on the same side of the surface as the incoming
  light, otherwise, is negative
• Image distance ? is positive when the image is on
  the same side of the surface as the outgoing
  light, otherwise is negative
• Radius of curvature of a spherical surface ? is
  positive when the centre is on the same side as
  the outgoing light, otherwise is negative
• Image height erected image is positive,
  inverted image is negative

17
Concave mirror

• Ray PV ? reflected back
• Ray PB - reflected to intersect optic axis on P?
• Provided the incidence angle is small, all rays
  from P intersect on axis at the same point P?
• image distance ? using plane geometry theorem
  exterior angle sum of two opposite interior
  angles, consider triangles PBC P?BC

eliminating ?
P ? object point C ? curvature centre P?? image
point V ? vertex of the mirror PV ? optic axis
? object-image relation
18
Focal point and focal length

• Focal point when the incoming rays are parallel
  to the optic axis, the reflected rays converge to
  a point F, the point is called focal point
• Focal length the distance from the vertex to the
  focal point, denoted by f

? object-image relation, spherical mirror
19
Two important cases

• Parallel incoming rays ? converge at focal point

• Incoming rays from focal point ? reflected rays
  are parallel to the optic axis

20
Image of extended object

• triangles of PQV P?VQ? are similar

• lateral magnification
• negative means the image is inverted relative to
  the object

21
Convex mirrors

• the relationship of object image is still valid
  to convex mirrors

Q

• but mind the sign of image distance

• the lateral magnification m, negative sign is
  because of negative image distance

• there are also focal point F and focal length f,
  but no rays pass though, which are called virtual
  focal point, and virtual focal length

22
Graphic methods for mirrors

• the position and size of the image can be
  determined by equations or simple graphical
  method? to find the points of intersection of a
  few particular rays (principle rays) and are
  reflected by mirrors
• a ray parallel to the axis
• a ray through (or proceeding toward) the focal
  point
• a ray along the radius
• a ray to the vertex

23
Useful tips to sketch diagram

• orient diagrams consistently
• light travels from left to right
• solid line for real light ray, doted line for
  extended line
• draw with ruler and measure the distance
• all the rays from a point would intersect at a
  point
• if the outgoing rays do not converge at a real
  image point, the image would be virtual, you have
  to extend backward to find the virtual point
• use the laws of reflection and refraction to
  check the direction of outgoing rays
• use the concept of focal point for rays pass
  though it or diverge from it

24
Refraction at a spherical surface

• triangles of PBC P?BC

P
25
Lateral magnification
for small angles
P
? whats the lateral magnification for a plane
refracting surface
26
Exercise

• where is the image for the case similar to the
  above but nagtnb?
• where is the image for the case similar to the
  above but the interface is concave?

27
Thin lenses

• most familiar and widely used optical device ?
  thin lens
• thin lens is an optical system with two
  refracting surfaces
• the refracting surfaces can be concave or convex
• has two spherical surfaces close enough together
  that the thickness can be neglected

diverging lens the lens thinner at the centre
than at the edge
converging lens the lens thicker at the centre
than at the edge
28
Converging lens

• properties of converging lens
• parallel incoming rays pass through lens converge
  to a point F2
• the rays passing through point F1 emerge from
  lens as a beam of parallel rays
• two focal points F1 F2
• centres of two spherical surfaces determine optic
  axis
• positive lens

29
Diverging lens

• properties of diverging lens
• parallel incoming rays pass through lens are
  diverged and appear come from point F2
• incident rays converging toward point F1 emerge
  from lens as a beam of parallel rays
• two focal points F1 F2, but reversed to
  converging lens
• centres of two spherical surfaces determine optic
  axis
• negative lens

30
Object-image relation
Q
similar triangles of PQO P?Q?O
similar triangles of AOF2 F2P?Q?
? object-image relation
31
Image features
? object-image relation

• If the object is outside the first focal point,
  sgtf, the image distance is positive, the image is
  real and inverted
• If the object is inside the first focal point,
  sltf, produces negative image distance, the image
  is virtual and erect
• Above equations are applicable to the diverging
  lens ? negative lens

Sketch diagrams to confirm above?
32
The Lensmakers equation

• the image formed by the first refracting surface
  can serve as the object for the second refracting
  surface

• ordinarily, third material is air, nanc1, and
  nb denoted as n
• s2 -s1

33
the Lensmakers equation
single unit
s s? replace s1 s2?
compare with the thin-lens equation
? lensmakers equation
Question what happens for the parallel light
consisting of red colour and violet colour hits
a converging lens?
34
Graphical methods for lenses

• the position and size of an image can be
  determined by graphical method drawing a few
  principle rays that diverge from a point of the
  object that is not on the optic axis
• the entire deviation is considered occurring at
  the midplane of the lens
• three principle rays
• a ray parallel to the optic axis
• a ray through the centre of the lens
• a ray through (or proceeding toward) the first
  focal point

35
exercises

• converging lens
• diverging lens

36
Optical Instrument ? camera

• basic elements
• converging lens normally has a few elements to
  correct aberrations
• light-tight box
• light sensitive film
• shutter to control exposure time

37
Camera - continued

• View angle
• telephoto lens, small angle, large image
• normal lens, 45 degree angle for 35 mm film,
  ideal to portrait
• wide-angle

38
Camera - continued

• Exposure ? the total light energy falls on the
  film or CCD, CMOS must be within certain limits
• Light intensity I is proportional to
• the area viewed through ? roughly proportional to
  1/f2
• to the effective area of the lens ? proportional
  to D2
• exposure can be controlled by aperture diameter
  shutter speed

• the ratio of f to D is called f-number
• the aperture varies by a factor of
• f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16

the intensity on film varies by 2
39
Microscope

• provides greater magnification, used to observe
  micro-subject (as small as 200 nm) for
• biology
• widely used for microelectronic and
  optoelectronic devices fabrication

diameter of mesa size 1 ?m
40
Microscope

• essential elements
• Stand
• light
• objective lens (converging)
• eyepiece (ocular, converging)

41

• image size and position
• objective lens forms a real enlarged image
• the image lies inside focal point of eyepiece,
  and forms enlarged virtual image

42
Microscope

• magnification
• angular size the angle subtended from object to
  the eye
• concept of angular magnification the ratio of
  the angle size with magnifier to the angle size
  without magnifier

• for simple magnifier (converging lens) ? the
  subject is placed at focal point, the virtual
  image is at infinity is comfortable to eye

normal reading distance 25 cm
assume subject is small enough
43
microscope

• for microscope

magnification of the objective
magnification of the eyepiece
ordinarily, object is close to focal point
44
Telescopes

• used to view the large objects at large distance
• normally telescopes use curved mirror as
  objective
• astronomical telescope
• objective forms an real, reduced image of the
  object, and this image serves as the object for
  the eyepiece lens to form an enlarged virtual
  image
• normally the image formed close to the focal
  point, and this image is located at the focal
  point to the eyepiece lens for comfortable view

45
Telescopes

• angular magnification

Binoculars 7?50, 7 ? angular magnification, 50
? objective lens diameter

• refracting telescope
• inverted image
• large f-number (f/D) causes a dim and
  low-intensity image
• chromatic aberrations ( dependence of focal
  length to wavelength)
• spherical aberrations (associated with the
  paraxial approximation)

46
Reflecting telescope

• Replace the objective lens by concave mirror to
  bring image to eyepiece
• free of chromatic aberrations
• spherical aberrations are easier to correct than
  with a lens
• mirror needs not to be transparent, so it can be
  made more rigid.

47
Reflecting telescope
48
Case 1 ? digital camera

• use CCD or CMOS to record image instead of film
• CCD charge coupled device
• CMOS complementary metal oxide semiconductor

49
CCD size

• no fundamental difference except the size of
  record medium
• full frame of the film for 135 camera 36?24 mm
• CCD size varies ? normally smaller than film
  frame
• for instance, three models of Cannon products
• what happens if take photos with different size
  of CCD?

50
view angle for different size CCD

• smaller CCD record part of the picture picked up
  by a bigger CCD
• or the view angle is getting smaller for smaller
  CCD

51
advantages for use of bigger size CCD

• ? any advantages for bigger size CCD
• Yes
• make more pixels ? higher resolution
• reduce noise ? more sensitivity
• professional digital cameras use bigger size of
  CCD ? normally similar to the size of film frame

52
How to choose lenses

• how to choose traditional lenses for digital
  cameras
• traditional lenses of film cameras can be used
  for digital cameras
• but the equivalent focal length changes ? the
  image taken by digital camera with CCD of 22X14.7
  mm and a lens with focal length of 85 mm looks
  like the image taken by a film camera with lens
  of 139 mm

53
Exercise on lenses

• ? the ideal focal length for film camera to take
  portrait is 85 mm, what focal length should be
  used to take portrait for digital camera with a
  CCD size of 22X14.7 mm
• The question can be simplified as which lens
  could be used for digital camera to form an image
  similar to the image formed by film camera with
  85 mm lens for a certain object with fixed
  distance