chapter 23:mirrors and lenses flat mirrors homework assignment : 20,24,42,45,51 image of a point...
TRANSCRIPT
Chapter 23:Mirrors and LensesFlat Mirrors
Homework assignment : 20,24,42,45,51
Image of a point source
P
P’
The reflected rays entering eyes lookas though they had come from image P’.
Light rays radiate from a point objectat P in all directions.
virtualimage
Image of a point source on a flat mirror (cont’d)
Image formation on a flat mirror
s’ (s) is the image (object) distance: |s| =|s’|
Sign Rules:(1) Sign rule for the object distance: When object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive. Otherwise it is negative.(2) Sign rule for the image distance:
When image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance s’ is positive. Otherwise it is negative.(3) Sign rule for the radius of curvature of a spherical surface:
When the center of curvature C is on the same side as the outgoing light, the radius of the curvature is positive. Otherwise it is negative.
Flat Mirrors
s’
Multiple image due to multipleReflection by two mirrors
h h’
m = h’/h=1lateral magnification
image is erectimage is virtual
Image of an extended object on a flat mirror
S’1
S’2
S’3
Flat Mirrors
Rotation of mirror
When a flat mirror is rotated, howMuch is the image rotated?
Flat Mirrors
Solution
x/2
(h-x)/2
h-x
x
What is the size of the smallest vertical plane mirror in which a womanof height h can see her full-length?
The minimum length of mirror fora woman to see her full height hIs h/2 as shown in the figure right.
Flat Mirrors
Example
Image Formed by Spherical Mirrors Concave and convex mirrors
Focal points at concave and convex mirror
Focal point or focus: Point F at which rays from a source point are brought together (focused) to form an image.Focal length: Distance f from mirror where focus occurs. f=R/2 where R is the radius of a spherical mirror.
Image Formed by Spherical Mirrors
Focal points at a concave mirror
s’
2
h )/(tan
)'/(tan
)/(tan
dRh
dsh
dsh
d
Rh
ssdifsh
sh
/
','/
/
fRss
12
'
11
object
image
If 2/', Rss
Image Formed by Spherical Mirrors
Image of an extended object at a concave mirror
Principle rays: Light rays that can be traced (more easily) from the source to the image:
1. Parallel to optical axis 2. Passing through the focal point
3. Passing through the center of curvature 4. Passing through the center of the mirror surface or lens
real image
Image Formed by Spherical Mirrors
Magnification of image at a concave mirror
h
h’
sf
f
s
s
h
hm
''
When s,s’ >0 , m<0 inverted s/s’<0, m>0 upright or erect
Image Formed by Spherical Mirrors
Example with a concave mirror
real image real image
real image virtual image
Image Formed by Spherical Mirrors
Example with a concave mirror
Image Formed by Spherical Mirrors
Image at a convex mirror
s s’f f
R
sf
f
s
sm
'
fRss
12
'
11
s positives’ negative (virtual image)R negativef negative
Image Formed by Spherical Mirrors
Magnification of image at a convex mirror
s’
'
'
s
satheight
s
satheight
For a convex mirror f < 0
sf
f
s
sm
fsss
s
satheight
satheightm
'
1
'
11,'
'
m > 1 magnified m < 1 minimizedm > 0 image uprightm < 0 image inverted
Image Formed by Spherical Mirrors
Refraction at a spherical surface Refraction at a convex spherical surface
For small angles sin 112211 nn
)/()/(
)/()(
1222111
2121
nnRnRRAB
ABfABBF
R
nn
nf )(
12
2
Refraction at a spherical surface Refraction at a concave spherical surface
For a concave surface, we can use the same formula
Rnn
nf )(
12
2
But in this case R < 0 and f < 0. Therefore the image is virtual.
Refraction at a spherical surface Relation between source and image distance at a convex spherical surface
s’
R
nn
s
n
s
n
s
AB
R
ABn
s
AB
R
ABn
ssABRAB
nn
122121
2121
')'
()(
'
)()(
For a convex (concave) surface, R >(<) 0.
Snell’s law
Refraction at a spherical surface Example of a convex surface
Refraction at a spherical surface Example of a concave surface
Refraction at a spherical surface Example of a concave surface
Refraction at a spherical surface Example of a concave surface
Convex Lens Sign rules for convex and concave lens:
Sign Rules:(1) Sign rule for the object distance: When object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive. Otherwise it is negative.(2) Sign rule for the image distance:
When image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance i is positive (real image). Otherwise it is negative (virtual image).(3) Sign rule for the radius of curvature of a spherical surface:
When the center of curvature C is on the same side as the outgoing light, the radius of the curvature is positive. Otherwise it is negative.
Convex Lens Lens-makers (thin lens) formula
surface 1
surface 2
Image due to surface 1:11
'11
'11
11111
nsnR
n
sR
n
s
n
s
s’1 becomes source s2 for surface 2:2
'2
'12
'22
11111
R
n
ssR
n
ss
n
2'211
11)
11(
R
n
snsnR
nn
s1 = s and s’2 = s’:
fRRn
ss
1)
11)(1(
'
11
21
s’
Parallel rays (s=inf.)w.r.t. the axis convergeat the focal pioint
R1>0 R2<0
Convex Lens Magnification
s’
PIIPSS
SSIIm
''
'/'
s
sm
'
sf
f
s
sm
'
same as for mirrors
Convex Lens Object between the focal point and lens
A virtual image
Convex Lens Object position, image position, and magnification
real inverted imagem < 1
real inverted imagem >1
virtual erect imagem >1
Lens Types of lens
Lens Two lens systems
Lens Two lens systems (cont’d)
Lens Two lens systems (cont’d)
Lens Two lens systems (cont’d)
Aberration
sphere paraboloid
Chromatic aberration
Gravitational lens
ExercisesProblem (focal length of a zoom lens)
Solution
I’r0 Q
f1 f2=-|f2|
r’0
d (variable)< s’2
f
(a)
f1
1101000'0
'00 /)()/( fdfrfdrrxrrrrx
(b) dff
dffs
dff
dff
fdf
ffd
sfsfdfds
12
12'2
12
12
12
21'22
'21
12
)(
)()(
1111
(c) dff
fff
dff
dff
df
fs
r
rf
f
r
s
r
12
21
12
12
1
1'2'
0
00'2
'0
)(
ray bundle
Find the effective focal length f of the combination lens.
dxr0
f1
s2