Hand with Reflection Sphere SelfPortrait in Spherical Mirror M'C' Escher

1
PH103
Lens combinations, Reflection, Spherical Mirrors
Dr. James van Howe Lecture 4
Hand with Reflection Sphere (Self-Portrait in
Spherical Mirror) M.C. Escher
March 17, 2008
2
Bonus Question
In what year did previous clip air on Network
television?

• 1975
• 1976
• 1977
• 1978

3
Problem 67, MCAT practice test 9
Changing which of the following will change the
focal length of the convex mirror in figure 2?

• Index of refraction of the mirror
• Radius of curvature of the mirror
• Position of the lens at B
• Focal length of the lens at B

4
Problem 68, MCAT practice test 9

5
Problem 69, MCAT practice test 9

• Converging rays
• Parallel rays in and out
• Reflected rays diverging
• Diverging rays

6
Qualitative Solution
Converging lens f10 cm,
Diverging lens f -10 cm,
20 cm
15 cm
Virtual Object
3
Light Source
Real Image
7
Quantitative Solution
20 cm
15 cm
-5 cm
I1, 02
3
I2
Light Source
20 cm
so
minus since virtual
Rays would form an image on a screen
8
Magnification
20 cm
15 cm
-5 cm
I1, 02
3
I2
Light Source
20 cm
9
Example HW3, Qualitative
Converging lens f18 cm,
2
3
Light Source
33 cm
12 cm
Diverging lens f -14 cm,
10
Example HW3, Quantitative
39.6 cm
Converging lens f18 cm,
2
I2
I1, 02
Light Source
33 cm
-27.6 cm
12 cm
-5 cm
Diverging lens f -14 cm,
-28.4 cm
Negative sign means virtual image
Even though rays seem real here, the image would
not form on a screen virtual
so
minus since virtual
11
Magnification
39.6 cm
Converging lens f18 cm,
I2
I1, 02
Light Source
33 cm
-27.6 cm
12 cm
-5 cm
Diverging lens f -14 cm,
-28.4 cm
12
Law of Reflection
Angle of incidence Angle of reflection
13
A mirror is a very special reflective surface
with a high degree of smoothness
A piece of paper
Flat mirror
Law of reflection always holds surface just
rough here reflection seems random
Good optical plane mirror has flatness lt l/5 or
lt 100 nm
14
Formation of a virtual image by a flat plane
mirror
Rays can be sketched back through the mirror to
form an image
Image is virtual, like a virtual image in a lens
system. The image appears to be behind the mirror
but we would not see it if we put a screen there.
15
Spherical Mirrors
16
Mirror Makers Equation
Like lens, the focal length of a spherical mirror
is related to its radius of curvature,R
lensmakers equation
Mirror surfaces the same, and no index
R
Slice it
Outside Surface Shiny
Convention is opposite lenses
Convex has negative focal length, Concave has
positive focal length
17
A spherical mirror transforms a plane wave into a
spherical wave
A plane wave is light from infinity, it focuses
at the focal point of the lens, f. Likewise, a
point source originating at the focal point is
imaged to infinity. A point source emanating from
the focus becomes a plane wave.
18
A spherical mirror transforms a plane wave into a
spherical wave
Incoming wave
Focal Point
Same thing is true for a convex mirror except the
original source is virtual. It is as if we had a
point source at the focal spot even though
nothing is there.
19
Rules for Tracing Mirrors
20
Mirror Equation

• Sign Conventions
• Use positive distances when the object, image, or
  focal point is on the reflecting side of the
  mirror (left for drawings)
• Use negative distances when the object, image, or
  focal point is on the non-reflecting side of the
  mirror (right for drawings)
• The height of the image is positive if the image
  is upright and negative otherwise

21
Concave Mirror
Object inside focal point Image always erect,
virtual, magnified
22
Concave Mirror
Object outside focal point Image inverted, real
23
Convex Mirror
Image always virtual, upright, and reduced
Car side-mirrors are convex for a larger field of
view, but they make objects look smaller and
therefore seem farther away
24
Dentist Problem, 11 HW3
Mirror must be in this configuration
25
Homework

• Ch23 12, 21