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35. Mirrors and images
Huygens’s Principle (analysis of wave propagation):
From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave.
Huygens’s Principle (analysis of wave propagation):
From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave.
Can be used to derive
Snel’s law and more
generally the properties
of mirrors and lenses
Huygens’s Principle (analysis of wave propagation):
From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave.
Examples: Fata Morgana (mirage)
Source: dailymail
Examples: Fata Morgana (mirage)
cold
hot
(hot air has lower index of refraction)
Source: dailymail
Examples: Fata Morgana (mirage)
Source: dailymail
es.wikipedia.org
Where is the image reflected in a typical mirror?
A. Mainly from the glass
B. Mainly from the metal behind the glass
C. Mainly from the back side of the glass covered by
black color
Reflection from a mirror
Plane Mirrors
Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if they
pass from a material of one index to another.
Direct images:
In air
Plane Mirrors
Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if the
pass from a material of one index to another.
Direct images:
In air
From inside material
Plane Mirrors
Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if the
pass from a material of one index to another.
Direct images:
In air
From inside material Mirror image:
Plane Mirrors
Constructing the image: Following the light rays to form an
image of an object.
Virtual image
Plane Mirrors
Constructing the image: Following the light rays to form an
image of an object.
Virtual image
Negative distance
What is the magnification of the mirror image (flat mirror)?
A. -1
B. 1
C. 0
D. Other
Plane Mirrors
Constructing the image: Following the light rays to form an
image of an object.
Negative distance
Magnification:
𝑚 =𝑦′
𝑦= −
𝑠′
𝑠
Object y: Image y’:
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓= 0 ⇒ 𝑠 = −𝑠′
f (the focal point) = infinity
Two important relations for mirrors:
Two concepts:
real and virtual
images
Plane Mirrors
Constructing the image: Following the light rays to form an
image of an object.
Which one is the real object?
A. Top one
B. Bottom one
C. None
Xinhua News Agency
Measuring 500 meters in
diameter, the radio telescope is
nestled in a natural basin within a
stunning landscape of lush green
karst formations in southern
Guizhou province. It took five years
and $180 million to complete
The telescope requires a radio
silence within a 5-kilometer (3-mile)
radius, resulting in the relocation of
more than 8,000 people from their
homes in eight villages to make
way for the facility.
Spherical Mirrors
The focal point is at half of the mirror’s radius of curvature. The focal length is the distance from the vertex to the focal point.
All incoming rays will converge at the focal point.
Spherical Mirrors
vertex
Spherical concave mirror
http://www.fas.harvard.edu
Image examples:
Possible images
Spherical Mirrors
Image properties:
Object
Image
Magnification:
𝑚 =𝑦′
𝑦= −
𝑠′
𝑠
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓
Concave mirror
Spherical Mirrors
I have a concave spherical mirror of radius 2m, I place an object at 4m from the mirror, what is
the magnification of the object?
A. M=1/3
B. M=-1/3
C. M=1
D. M=-1
E. M=3
F. M=-3
Image examples:
Object far away from mirror
Object
Image
Magnification:
𝑚 =𝐼𝑚𝑎𝑔𝑒
𝑂𝑏𝑗𝑒𝑐𝑡= −
𝑠′
𝑠Object-image relationship:
1
𝑠+1
𝑠′=1
𝑓
𝑠s’
Spherical Mirrors
Image examples:
Object far away from mirror
Object
Image
Magnification:
𝑚 =𝐼𝑚𝑎𝑔𝑒
𝑂𝑏𝑗𝑒𝑐𝑡= −
𝑠′
𝑠=
𝑓
𝑓 − 𝑠< 0
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓
𝑠s’
Spherical Mirrors
Image examples:
Object far away from mirror
Object
Image
Magnification:
𝑚 =𝐼𝑚𝑎𝑔𝑒
𝑂𝑏𝑗𝑒𝑐𝑡= −
𝑠′
𝑠=
𝑓
𝑓 − 𝑠< 0
and |m|<1
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓𝑠
s’
Spherical Mirrors
I have a concave spherical mirror of radius 4m, I place an object at 1m from the mirror, what is
the magnification of the object?
A. M=1/2
B. M=-1/2
C. M=1
D. M=-1
E. M=2
F. M=-2
Image examples:
Object close to mirror
ObjectImage
Magnification:
𝑚 =𝐼𝑚𝑎𝑔𝑒
𝑂𝑏𝑗𝑒𝑐𝑡= −
𝑠′
𝑠=
𝑓
𝑓 − 𝑠> 1
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓
Spherical Mirrors
s s’
Image examples:
Object close to mirror
ObjectImage
Magnification:
𝑚 =𝐼𝑚𝑎𝑔𝑒
𝑂𝑏𝑗𝑒𝑐𝑡= −
𝑠′
𝑠=
𝑓
𝑓 − 𝑠> 1
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓
Spherical Mirrors
s s’
For example:
R=4=>f=2; s=1; 1+1/s’=1/2=>s’=-2; m=2
Position of object Position of image Nature of image
dO < F Behind the mirror Virtual, enlarged, upright
dO = F No image No image, rays reflected parallel
F < dO < C Beyond C Real, enlarged, inverted
dO = 2F At C Real, same size, inverted
dO > 2F Between F and C Real, reduced, inverted.
dO = ∞ At F of size zero
Image examples:
All possibilities with
Concave mirror of radius C
physics.tutorvista.com
Spherical Mirrors
Double lens trick
dev.physicslab.org
Spherical Mirrors
Convex mirror
Spherical Mirrors
Convex mirror (negative focal length):
Magnification:
𝑚 =𝑦′
𝑦= −
𝑠′
𝑠
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓
f<0
(s>0 and s’<0 –> virtual image)
Spherical Mirrors
Convex mirror (negative focal length):
Magnification:
𝑚 =𝑦′
𝑦= −
𝑠′
𝑠
Object-image relationship:1
𝑠+1
𝑠′=1
𝑓
f<0
(s>0 and s’<0 => image is opposite to outgoing ray
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