index of refraction index of refraction of a medium is defined in terms of the speed of light in...
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Index of Refraction
Index of refraction of a medium is defined in terms of the speed of light in this medium
v
cn
In general, the speed of light in any material is less that its speed in vacuum.
v1 T = 1 , v2 T = 2
1 2
Hence
1
2
2
1
2
1
n
n
v
v
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reflection and refraction
incident ray
reflected ray
refracted ray
1 ’1
2
angle of incidence
angle of reflection
angle of refraction
The law of reflection:
The reflected ray lies in the plane of incidence and the angle of reflection ’1 is equal to the angle of incidence ’
’1 = 1
The law of refraction:
The refracted ray lies in the plane of incidence and the angle of refraction 2 is related to the angle of incidence 1 by
n1 sin 1 = n2 sin 2
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the law of reflection and the law of refraction
1
C
D
A
A’
’1
AC
AD
AC
C'A1sin 1'sin
11 '
2
B
1
2
v
v
C'A
AB
2sinACAB
1sinACC'A
2
1
n
n
2
1
1
2
n
n
sin
sin
1222 sinnsinn
ADC'A
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Prism and Dispersion
Index of refraction of a material is a function of the wavelength
50
60
deviation angle
angle
dispersion angle
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seeing objects
In order to be seen, an object must send light from each of its points in many directions. The eye collects some of the light emitted from a point allowing the brain to interpret the location of the point.
In some situations diverging rays are interpreted as originating from a single point creating an image of a point.
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plane mirror
If the rays are emitted from a point (real object) or converge to a point (virtual object), after they are reflected by the mirror, the rays or their extensions meet at a point to form an image.
object(real)
image(virtual)
s s’
reflecting surface
image(real)
s s’
object(virtual)
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spherical mirror
If the rays are emitted from a point (real object) or converge to a point (virtual object), after they are reflected by the mirror, the rays or their extensions meet approximately at a point to form an image.
O(object) parallel ray
(object) chief ray
(object) normal ray
(image) normal ray(image)
focal ray
(image) chief ray
(image) parallel rayC
F principalaxis
I
(object) focal ray
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the mirror equation: O
C
I
0
s’
h
h’
s
R
's
s'sR
Rs
'h
h
R
2
s
1
's
1
from geometrical considerations:
R's'ss'sssR
'ss2R'ssR
f
1
For a concave mirror the focal length is positive and for a convex mirror the focal length is negative.
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thin spherical lens
If the rays are emitted from a point (real object) or converge to a point (virtual object), after they are refracted by the lens, the rays or their extensions meet approximately at a point to form an image.
O(object) parallel ray
(object) chief ray
Fo
I
(object) focal ray
(image) focal ray
(image) parallel ray
Fi
(image) chief ray
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thin lens equation
O
Fo
I
Fi
h
h’
s s’
f
's
s
'h
h
f's
f
fss's'fs
s'sfs'fs f
1
's
1
s
1
positive object’s position positive image position
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lens maker's equationR1>0
R2<0
n0
n
The focal length of a thin-lens is determined by the curvatures of the two surfaces, the index of refraction of the lens material, and the index of refraction of the surrounding medium
210 R
1
R
11
n
n
f
1
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Magnification
Object
Image
The magnification is defined as the ratio of the image height to the object height.
Mhh
'
s
's
h
s h’
s’
Fo
Fi
If the orientation of the image is the same as that of the object, a positive value is assigned to the magnification.
For an inverted image the magnification is negative.
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angular magnification
The angular magnification (magnifying power) of an instrument is defined as the ratio of the "angular size" of the final image and the "angular size" of the observed object.
m '
N
example: magnifying glass
h
h’ ’
s
s
Nm
N
'h'
Ns
Nh
s
N
N
h
s
N
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vision
cornea
retina
lens
Fo
Fi
If the object is between the near and the far point of the eye, its lens the eye muscles adjust the focal length of the lens to form a real image on the retina.
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two thin lenses in contact
I1
F1o
F1i
F2o
F2i
O1
111 f
1
's
1
s
1
O2
222 f
1
's
1
s
1
1s
's2 's1
s
2s's
11 f
1
's
1
s
1
21 f
1
's
1
's
1
11 f
1
f
1
's
1
s
1
The system of two close lenses behaves like a single lens with a focusing power equal to the sum of the focusing powers of each lens separately.
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compound microscope
objective
eye piece
L
specimen
'
m ef
'h h
L
ff
Lh
eo eo
2
ff
L
angular magnification
The objective produces the first (real) image almost at the focal point of the ocular. The eye piece form the final (virtual) image between the near and the far point of the observer’s eye.
L
h
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Keplerian telescope
The objective produces the first (real) image almost at its focal point and the focal point of the ocular. The eye piece form the final (virtual) image between the near and the far point of the observer’s eye.
h’
angular magnification
'
m ef
'h
of
'h
e
o
f
f