Optical Geometrics dial 22-XA

8/9/2019 Optical Geometrics dial 22-XA

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1.1 Flat MirrorThe nature of images that are produced by flat mirrors

can be summarized as follows :

* The images are upright (same as the objects)

* The images have the same size as the objects

* The distance of the objects to the mirror is equal to

the images to the mirrors

* Reflected images are virtual images


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The characteristic of concave

mirror are if the parallel rays hitthe surface of the mirror, the

reflected rays would converge

at a point. This is also called the

focal point (f).The normal line on every

point on a concave mirror is

called the center of curvature of

a mirror (R).The relation between focal

length and center of curvature

can be written as :

f = R


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i) Rays that come in parallel

with the main axis arereflected through a focal

point

ii) Rays that come through a

focal point are reflectedparallel with the main axis

iii) Rays that come through

the curvature of mirror are

reflected back through thatcurvature


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Convex mirrors are curved mirrors that reflect the raysthat come to mirrors outward and seems to come from the

focal point. The parallel rays that come to the convex mirror

are reflected divergently.


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i) The rays that come parallel

to the main axis are

diverged. The reflected rays

seem to come from the focal

point

ii) The rays that are come

toward the focal point are

reflected in parallel with the

main axis

iii) The rays that are comethrough the curvature are

reflected back through the

curvature


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By applying the properties of a concave and convex mirror,the image of an object can be drawn easily. There is a

relationship between an objects position and its image,

which are formed. The relation can be written as :

1 1 1

s s f + =

NB :NB :

s : the distance of an object to the

mirror (cm)

s : the distance of an image to the

mirror (cm)

f : the focal length (cm)

R : center of curvature (cm)

1 1 2

s s R+ =


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The size of an image that is formed by a mirror can looklarger or smaller than its object. Therefore, we define

linier magnification as a ratio of image and object size.

The linier magnification can be expressed as the following

equation :NB :NB :

M : the linier magnification

s : the distance of an object to

the mirror (cm)

s : the distance of an image to

the mirror (cm)

h : object size (cm)

h : image size (cm)

M= =s

s h

h

M =s

=f

s-fs


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s (+) Object in front of mirrorss (-) Object behind of mirror

s (+) Image in front of mirror

s (-)

Image behind of mirrorf (-) Concave mirror

f (+) Convex mirror

M > 1 Magnified

M < 1 Diminished


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Concave Mirrors

Object position Image Orientation Image Size TypeofImage

Larger than 2f Inverted Diminished (smaller) Real

On 2f point Inverted Same size Real

Between f and 2f Inverted Magnified (larger) RealLess outside f Inverted Infinity Real

Less inside f Upright Infinity Virtual

Between f and 2f Upright Magnified (larger) Virtual

Convex Mirror

Object position Image Orientation Image Size TypeofImage

Any position Upright Diminished (smaller) Virtual


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To draw the image that happen in 2 faced set of mirror,direction of rays are took from an objectto the firstmirror, then reflected to the other mirror so can be drawnthe last image from the second mirror. The followingequation :

Where :

d = distance between mirror 1 and mirror 2

s1 = distance of first image to the first mirror

s2 = distance the second object to the second mirror

Mtot = Total magnification

M1 = Magnification of the first mirror

M2 = Magnification of the second mirror

d = s1 + s2 Mtot = M1 x M2


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Lenses are transparent mediums where one or bothsides are curved mirrors.

The curved surface of the lens causes the light that falls

on the surface of the lens to refract in different directions.

As a result, when light leaves the lens, it gathers in onespot or spreads in different directions. This is depend on

the curvature of the curvature of the surface of the lens.


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The physical

characteristics of convex lens

are that they are thickest at

the center of their lens and

their edges are thinner than

at their center.

Kinds ofConvex Lens


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i) The incident rays that areparallel to the main axis of

the lens are refracted

through the focal point on

the other side of the lens

ii) The incident rays that

come through the focal

point are reflected parallel

to the main axis of the

lensiii) The incident rays that

come through center of

the lens is transmitted

without refraction


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One of the physical

characteristic of concave lens

are that is thinnest at the

middle of the lens. To the

edge, the lens thickness

increases.The incident beams that

are parallel to the main axis

are reflected divergently.

They seem to be derivedfrom the first focal point of

lens.

Kinds ofConcave Lens


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i) The incident beams that

are parallel to the main

axis are refracted

divergently. They seem to

be derived from the first

focal point of the lensii) The rays that come toward

the other focal point are

refracted in a parallel

fashion to the main axisiii) The incident rays that pass

through the center of the

lens are transmitted

without being refracted


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By applying the properties of a concave and convex lens, theimage of an object can be drawn easily. There is a

relationship between an objects position and its image,

which are formed. The relation can be written as :

1 1 1

s s f + =

NB :NB :

s : the distance of an object to the

mirror (cm)

s : the distance of an image to the

mirror (cm)

f : the focal length (cm)

R : center of curvature (cm)

1 1 2

s s R+ =


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The size of an image that is formed by a lens can look largeror smaller than its object. Therefore, we define linier

magnification as a ratio of image and object size. The

linier magnification can be expressed as the following

equation :NB :NB :

M : the linier magnification

s : the distance of an object to

the mirror (cm)

s : the distance of an image to

the mirror (cm)

h : object size (cm)

h : image size (cm)

M= =s

s h

h

M =s

=f

s-fs


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s (+) Object in front of mirrorss (-) Object behind of mirror

s (+) Image in front of mirror

s (-) Image behind of mirror

f (+) Convex lens

f (-) Concave lens

M > 1 Magnified

M < 1 Diminished


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In optics, the characteristic of lens is usually expressed inoptical power quantity. The greater optical power of the lens,

the closer position of image to the lens.

The optical power of lens is defined as :

or

where P is Optical power (dioptri/D)

1

f= P (m)

100

f= P (cm)


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Convex Lens

Object Position Image Orientation Image Size Type of Image

Between lens andf Upright Magnified (larger) Virtual

Betweenfand 2f Inverted Magnified (larger) Real

Far away (s > 2f) Inverted Diminished (smaller) Real

Concave Lens

Object Position Image Orientation Image Size Type of Image

Any position in front

of lens

Upright Diminished (smaller) Virtual


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To draw the image that happen

in 2 faced set of lenses,

direction of rays are took

from an objectto the first

lens, then refracted to the

other lens, so can be drawnthe last image from the

second lens. The following

equation :

d = s1 + s2

Mtot = M1 x M2

Where :

d = distance between mirror 1 and

mirror 2

s1 = distance of first image to the first

mirror

s2 = distance the second object to the

second mirrorMtot = Total magnification

M1 = Magnification of the first mirror

M2 = Magnification of the second

mirror


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If that lenses are combined together (d= 0), so that lenses can be

replaced with equivalent lens, by equation :


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If the beam comes perpendicular to the surface of the water, it

enters the water without changing the direction If the beam comes to the surface at a different angle, the

propagation line breaks at the surface (boundary between

water and air). The change in the propagation line at the

boundary of two media is known as refractionBased on the above explanation, we conclude that the refraction

occurs if :

i) The speed of light in two media is different

ii) The propagation line of the incidence light is not

perpendicular to the boundary between two media

The relation between incidence and refractive angles when a light

beam passes through a boundary of two medium is given by

Snells Law:


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The relation between incidence and refractive angles when a

light beam passes through a boundary of two medium is

given by Snells Law:

n1 sin 1 = n2 sin 2

Where

n1

Index of refraction of incident material

sin 1Angle of incidence (degrees)

N2 Index of refraction of refractive material

sin 2 Angle of refraction (degrees)

v = .fSo n1 sin 1 = n2 sin 2

n12 = = =n1

n2

v1

v2

2f

1f


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Apparent Elongation and Apparent Shortening

When we look down into a pool of water from above, the poolooks less deep than it really is.

n1 n1 h hh h

Apparent Elongation Apparent Shortening

h=

n2x

cos 2

h n1 cos 1


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Where :

n1 : refractive index of

medium 1

n2 : refractive index ofmedium 2

n1n2 n2n1s

+s

=R


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Second Focus First Focus

s = f1..s =

f1 = (n1/n2 n1)x R

s =

f2 = (n2/n2 n1)x R


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In optics, a thin lens is a lens with a thickness (distance along theoptical axis between the two surfaces of the lens) that is negligible

compared to the foca length l of the lens.Lenses whose thickness is

not negligible are sometimes called thick lenses.

The thin lens approximation ignores optical effects due to the

thickness of lenses and simplifies ray tracing calculations. It is often

combined with the paraxial approximation in techniques such as ray

transfer matrix analysis.


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The focal length of a lens in aircan be calculated from the

lensmaker's equation:[10]

Where :

fis the focal length of the lens, n is the refractive index of the lensmaterial, R1 is the radius of curvature of the lens surface closest

to the light source, R2 is the radius of curvature of the lens surface

farthest from the light source, and d is the thickness of the lens

(the distance along the lens axis between the two surface

vertices).

1

+

1

= (n1

- 1 ) (1

+

1

)s s nmedium R1 R2


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Total internal reflection is an optical phenomenon thatoccurs when a ray oflight strikes a medium boundary at

an angle larger than a particular critical angle with respect

to the normal to the surface. If the refractive index is

lower on the other side of the boundary, no light can passthrough and all of the light is reflected. The critical angle

is the angle of incidence above which the total internal

reflection occurs.

When light crosses a boundary between materials withdifferent refractive indices, the light beam will be partially

refracted at the boundary surface, and partially reflected.


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However, if the angle of incidence is greater (i.e. the ray is closer to

being parallel to the boundary) than the critical angle the angle of

incidence at which light is refracted such that it travels along the

boundary then the light will stop crossing the boundary altogetherand instead be totally reflected back internally. This can only occur

where light travels from a medium with a higher [n1=higher refractive

index] to one with a lower refractive index [n2=lower refractive index].

For example, it will occur when passing from glass to air, but not when

passing from air to glass.

sin c =n2

n1


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= 2 + 3

D = 1 + 4

where :

: angle of refractor


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A plate of glass with

thickness t. The direction ofthe incident beam and the

beam leaving the material at

the opposite surface are the

same, but they are different

in the propagation line. The

propagation lines are parallel

but one is displaced from the

other.

Therefore, the

displacement of the

propagation line of the

refracted beam can be

defined :

t =d sin ( 1 - 2 )

cos 2

t =d sin ( 1 - 2 )

cos 2

For n2 >n1

For n1 >n2

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Optical Geometrics dial 22-XA

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