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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

Change of wavelength

- the waves get squeezed from smaller refractive

index material to greater one - or stretched reversely

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

Spreading of optical square pulses

- Laser (LED) generated pulses transit through

optical fibre

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

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

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

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

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

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

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

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

Derive of Snells law

- From triangles OOA OBA

? Snells law

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

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

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

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

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

Two important cases

- Parallel incoming rays ? converge at focal point

- Incoming rays from focal point ? reflected rays

are parallel to the optic axis

Image of extended object

- triangles of PQV P?VQ? are similar

- lateral magnification
- negative means the image is inverted relative to

the object

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

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

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

Refraction at a spherical surface

- triangles of PBC P?BC

P

Lateral magnification

for small angles

P

? whats the lateral magnification for a plane

refracting surface

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?

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

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

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

Object-image relation

Q

similar triangles of PQO P?Q?O

similar triangles of AOF2 F2P?Q?

? object-image relation

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?

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

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?

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

exercises

- converging lens
- diverging lens

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

Camera - continued

- View angle
- telephoto lens, small angle, large image
- normal lens, 45 degree angle for 35 mm film,

ideal to portrait - wide-angle

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

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

Microscope

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

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

and forms enlarged virtual image

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

microscope

- for microscope

magnification of the objective

magnification of the eyepiece

ordinarily, object is close to focal point

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

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)

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.

Reflecting telescope

Case 1 ? digital camera

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

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?

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

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

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

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

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