Physics 11 Final Essay-Nathanael Li, Zhimo-Block A.pdf

Lens and Mirrors
Review, Development, Application
Ms Shi
Physics 11, Block A
Nathanael Li, Zhimo
10 January 2022
Physics 11 Final Essay 1

Introduction:
After a period of study, we have some physical knowledge about mirrors
and lenses. In the next essay, I will use 5 whats and 3 hows to show what I
have learned in "Mirrors and Lenses"
What is Lens?
A lens is a transparent (glass) optical device with a curved surface.
And lens have two types:
Converging (convex) lens Diverging (concave) lens
A converging lens is thicker at the middle than at its ends.
These are also known as convex lenses.
A diverging lens is a lens that is thinner in the middle than it is on its ends.
These are also known as concave lenses.

What is Mirrors?
A mirror is an object that re
fl
ects an image. Light that bounces o
ff
a
mirror will show an image of whatever is in front of it, when focused
through the lens of the eye or a camera.
And Mirrors have 3 types:
Convex (converging) mirrors Flat mirrors Concave (Diverging) Mirror
A concave mirror is a concave side that re
fl
ects
A convex mirror is a convex side that re
fl
ects
A plane mirror is one side of a mirror that re
fl
ects
What are their principles?
Converging (convex) lens:
According to the principle of light refraction, when the light is incident vertically,
the light does not refract, so the ray on the main optical axis of the convex lens
does not refract, but other rays will refract.
Discuss in three cases:
Case 1: When the rays are parallel or nearly parallel.
When parallel rays enter the convex lens from the front, all
the rays that are not on the main optical axis will be
refracted, and after the refraction, all the rays will converge
at a point behind the convex lens, and the convergence point
depends on the focal length of the convex lens.
Case 1
f’(focus)

Case 2: When the light is emitted from a point light source.
When the point light source enters the convex lens from the
front, all the light rays will become parallel to the main optical
axis after being refracted by the lens, and will be emitted from
the back of the concave lens to become parallel light.
Case 3: Converging light into a convex lens
When the converging light enters the convex lens, after the lens
is converged, all the light will be more deviated to the main
optical axis, exit from the back of the concave lens, and
fi
nally
complete the convergence in advance before the focus.
Diverging (concave) lens:
According to the principle of refraction of light, when the light enters vertically,
the light does not refract, so the ray on the main optical axis of the concave lens
does not refract, but other rays will refract.
Discuss in three cases:
When parallel rays enter the concave lens from the front, all rays not on the
main optical axis will be refracted, and after the
refraction, all rays will be refracted away from the
main optical axis, and all the outgoing rays will be
extended in reverse and converge in front of the
concave lens At one point, the point of convergence
depends on the focal length of the concave lens.
Case 2
Case 3
f’(focus)
Case 1
f (focus)

When the point light source enters the concave lens from the front, the light is
refracted by the lens, and all the light rays will be refracted
further away from the main optical axis, and will be
emitted from the back of the concave lens. The
reverse extension of the incident light will be parallel
to the main light in front of the concave lens The axis
is re
fl
ected into a virtual image of a point light source, and the
point of convergence depends on the focal length of the
concave lens.
Case 3: Converging light into a concave lens
When the condensed light enters the concave lens, after
correction by the lens, all the light rays will become parallel to
the main optical axis and exit from the back of the concave lens.
Concave (converging) mirrors:
According to the principle of refraction of light, when the light is incident
vertically, the light does not refract, so the ray on the main optical axis of the
concave mirror emits vertical re
fl
ection, but other rays will be refracted.
There are two situations to discuss:
When parallel rays are emitted from the front to the concave
mirror, except for the vertical re
fl
ection on the main optical
axis of the concave mirror, all other rays that are not on the
main optical axis will be refracted, and after the refraction,
all the rays will converge in the front of the concave mirror.
One point, the point of convergence depends on the focal length of
the concave mirror.
When the point light source emits divergent light from the
front and encounters the concave mirror, the light is
corrected by the re
fl
ection of the mirror, and all the light rays will
Case 2
Point light
source
Case 3
f (focus)
Case 1
f (focus)
Case 2

become parallel to the main optical axis, and then emerge from the concave
mirror and become parallel light.
Convex (Diverging) Mirror
According to the principle of refraction of light, when the light is incident
vertically, the light does not refract, so the ray on the main optical axis of the
convex mirror emits vertical re
fl
ection, but other rays will be refracted.
There are two situations to discuss:
When parallel rays are emitted from the front to the convex mirror,
except for the vertical re
fl
ection on the main optical axis of the convex
mirror, all other rays not on the main optical axis will be refracted, and
after the refraction, all the rays will be deviated from the main optical axis.
directional refraction.
Case 2: When the light is convergent light.
When the convergent light source encounters the convex mirror
from the front, the light is corrected by the re
fl
ection of the
mirror, and all the light rays will become parallel to the main
optical axis, and then emerge from the convex mirror and
become parallel light.
How do they work?
Converging (convex) lens:
The principle rays for converging lenses are as follows:
1) A ray traveling parallel to the principle axis will refract through the principle
focus.
2) A ray travelling through the secondary focus will refract parallel to the
principle axis.
3) A ray travelling through ‘o’ will continue on its path.
f’ (focus)
Case 1
f’ (focus)
Case 2

Tips：One focal length is divided into virtual and real; twice the focal length is
divided into size; twice the focal length makes the object and the image the same
size; the object is closer to the lens and the close image is farther away and
becomes larger, and vice versa
The real image is down, the virtual image is up.
f (focus)
2f
inverted, real
inverted, real
inverted, real
No image
Upright, virtual

Diverging (concave) lens:
The principle rays for a diverging lens are as follows:
1) A ray that travels parallel to the principle axis appears to refract from the
principle focus.
2) A ray that travels towards the secondary focus will refract parallel to the
principle axis.
3) A ray that travels through ‘o’ will continue on its path.
Upright, virtual
Upright, virtual
Upright, virtual

Tip: the concave lens only presents the vertical reduction of the virtual image
Concave (converging) mirrors & Convex (diverging) mirrors:
The ray diagram for image formation by mirrors can be drawn by taking any
two of the following rays. The point where these two rays meet or appear to be
coming from the point will be the image point which determines the position of
image.
1. Ray striking the pole: The ray of light striking the pole of the mirror at
an angle is re
fl
ected back at the same angle on the other side of the principal
axis.
2. Parallel ray: For concave mirror the ray parallel to the principal axis is
re
fl
ected in such a way that after re
fl
ection it passes through the principal
focus. But for a convex mirror the parallel ray is so re
fl
ected that it appears to
come from principal focus.
3. Ray through centre of curvature: A ray passing through the centre
of curvature hits the mirror along the direction of the normal to the mirror at
that point and retraces its path after re
fl
ection.
4. Ray through focus: A ray of light heading lowards the focus or incident
on the mirror after passing through the focus returns parallel to the principal
axis.
Upright, virtual
Upright, virtual

Concave mirror: Convex mirror
The position, nature and size of the image formed in concave mirror and
convex mirror can be summarised as:
Object Position Image Position Nature Size
Concave Mirror
1 Between P & F Behind the mirror Virtual Larger
2 At F At in
fi
nity Real Enlarged
3 Between F & 2F Beyond 2F Real Larger
4 At 2F At 2F Real Same size
5 Beyond 2F Between F & 2F Real Smaller
6 At in
fi
nity At F Real Diminished
Convex Mirror
7 Anywhere Between P & F Virtual Smaller

What is the di
ff
erence of lens and mirrors?
The biggest di
ff
erence between a mirror and a lens is that a mirror can only
re
fl
ect light, but a lens allows light to pass through.
The mirror is a silver-backed glass that produces an image on one surface
only by re
fl
ection. Whereas a lens is a transparent substance that produces an
image by refraction on either of the two surfaces.
And the laws they use are also di
ff
erent. The law used by mirrors is Laws of
re
fl
ection, and the law used by lenses is Laws of refraction.
P. S. : Note the di
ff
erence between "re
fl
ection" and "refraction"
What are theirs equations?
The relationship between the position of the image and the object and the focal
length is:
Where:
f = focal length
di = image distance
do = object distance
All distances are measured from the mirror (at the vertex) along the principle axis.
The ratio of the image height to the object’s height gives us the magni
fi
cation
Where:
1
f
=
1
di
+
1
do
m =
hi
ho
=
−di
do

m = magni
fi
cation
hi = image height
ho = object height
How to calculate?
Example 1: You look at the re
fl
ection of an insect that is 8mm long in a concave mirror
and the image you see is 28 mm long. What is the magni
fi
cation (M)
Example 2: A nail 4.00 cm tall stands 15.0 cm from the focal point of a converging mirror.
If the focal length of the mirror is 20.0cm, how tall is the image? (hi = -5.3 cm)
Do=15cm+20cm = 35cm
di=
Because , then hi= -5.3cm
How do Lens and Mirrors apply into our life?
Mirrors:
Personal grooming
Mirrors are commonly used as aids to personal grooming. They may range from small
sizes, good to carry with oneself, to full body sized; they may be handheld, mobile,
fi
xed
or adjustable. A classic example of the latter is the cheval glass, which may be tilted.
Safety and easier viewing
Convex mirror placed at the parking garage.
Convex mirrors provide a wider
fi
eld of view than
fl
at mirrors, and are often used on
vehicles, especially large trucks, to minimize blind spots. They are sometimes placed at
road junctions, and corners of sites such as parking lots to allow people to see around
m =
hi
ho
=
28mm
8mm
= 3.5
1
di
=
1
f
−
1
do
=
1
20
−
1
35
=
3
140
140
3
hi
h o
= −
di
do

corners to avoid crashing into other vehicles or shopping carts. They are also sometimes
used as part of security systems, so that a single video camera can show more than one
angle at a time. Convex mirrors as decoration are used in interior design to provide a
predominantly experiential e
ff
ect.
Mouth mirrors or "dental mirrors"
Mouth mirrors or "dental mirrors" are used by dentists to allow indirect vision and lighting
within the mouth. Their re
fl
ective surfaces may be either
fl
at or curved. Mouth mirrors are
also commonly used by mechanics to allow vision in tight spaces and around corners in
equipment .
Rear-view mirrors
Rear-view mirrors are widely used in and on vehicles (such as automobiles, or bicycles),
to allow drivers to see other vehicles coming up behind them. On rear-view sunglasses,
the left end of the left glass and the right end of the right glass works as mirrors.
One-way mirrors and windows
Signalling
With the sun as light source, a mirror can be used to signal by variations in the
orientation of the mirror. The signal can be used over long distances, possibly up to 60
kilometres (37 mi) on a clear day. This technique was used by Native American tribes and
numerous militaries to transmit information between distant outposts.
Mirrors can also be used for search to attract the attention of search and rescue parties.
Specialized type of mirrors are available and are often included in military survival kits.
Technology
Televisions and projectors
Microscopic mirrors are a core element of many of the largest high-de
fi
nition televisions
and video projectors. A common technology of this type is Texas Instruments' DLP. A
DLP chip is a postage stamp-sized microchip whose surface is an array of millions of
microscopic mirrors. The picture is created as the individual mirrors move to either re
fl
ect
light toward the projection surface (pixel on), or toward a light absorbing surface (pixel
o
ff
).
Other projection technologies involving mirrors include LCoS. Like a DLP chip, LCoS is a
microchip of similar size, but rather than millions of individual mirrors, there is a single
mirror that is actively shielded by a liquid crystal matrix with up to millions of pixels. The
picture, formed as light, is either re
fl
ected toward the projection surface (pixel on), or
absorbed by the activated LCD pixels (pixel o
ff
). LCoS-based televisions and projectors
often use 3 chips, one for each primary color.
Large mirrors are used in rear projection televisions. Light (for example from a DLP as
mentioned above) is "folded" by one or more mirrors so that the television set is
compact.
Solar power

The concave mirror can gather light energy and heat energy. In the Athens Olympic
Games, the stove that ignited the torch is a solar stove composed of a huge concave
mirror. one of the places. In addition to being used for ignition, solar cookers can also be
used to boil water and cook.
Lens:
The Human Eye and Corrective Lenses
Many people do not have perfect vision; that is, a lot of people have eyes whose lenses
do not focus light properly on the retina. Two well-known vision problems correctible via
eyeglasses are nearsightedness (picture (a) below) and farsightedness (picture (c)).
Nearsightedness focusses rays of light in front of the retina, while farsightedness
focusses rays behind the retina. A diverging lens can correct nearsightedness by bending
incoming light rays outwards, so that the eye's lens (which usually bends incoming rays
too much) focusses the light closer to the retina (picture (b)). A converging lens similarly
corrects farsightedness (picture (d)
A greatly simpli
fi
ed view of the human eye is shown above. The pupil is a little hole which allows light to pass into the
eye. Behind the pupil lies the eye's lens. Muscles in the eye control the size of the pupil and the shape of the lens,
thereby adjusting the amount of light that enters they eye and the focus of the lens. The retina is a sensitive layer of
nerves at the back of the eyeball; incident light upon the retina is translated into a coherent image by the brain.
Retina
Lens
A normal human eye model (simpli
fi
ed)
(a)
(c) (d)
(b)

Magnifying Glasses
In our study of lenses, we saw that if the source was placed within a focal length of a
converging lens, the lens yielded a magni
fi
ed image on the same side of the lens as the
source. This is, of course, the detective's best friend, the magnifying glass.
The amount of magni
fi
cation, as we know from our treatment of lenses, depends on the
distance of the source from the lens, and the refractive index of the lens material.
Cameras
Cameras, unsurprisingly, work on similar principles as the eye.
The aperture, which lets light into the inside of the camera, corresponds to the pupil. The
system of lenses in a camera performs the same function as the lens of the eye.
However, whereas the lens of the eye changes shape to change focus, glass lenses are
not very forgiving of shape changes. Instead, the lens system can be slid along its optical
axis in order to focus on the
fi
lm. Of course, the
fi
lm plays the role of the retina. In
addition, cameras have a shutter, which opens and closes quickly so that the
fi
lm does
not get inundated with light. This produces a more or less clear image of the instant that
the photographer shoots.
Also you glasses, the microscope, the telescope, etc.
Citations (APA7 Style):
Applications of Mirrors and Lenses. (n.d.). Personal.math.ubc.ca. Retrieved January 11, 2022, from
https://personal.math.ubc.ca/~cass/courses/m309-01a/chu/Applications/apps.htm
Convex & Concave Lenses - Pass My Exams: Easy exam revision notes for GSCE Physics<. (2018).
Passmyexams.co.uk. http://www.passmyexams.co.uk/GCSE/physics/concave-lenses-convex-
lenses.html
Image Formation by Spherical Mirrors - Study Page. (n.d.). Www.studypage.in. Retrieved January 11,
2022, from https://www.studypage.in/general-science/image-formation-by-spherical-mirrors
Lenses in Optics - Applications | Types of Lenses | Physics. (n.d.). BYJUS. https://byjus.com/physics/
lenses-in-optics/
Lens. (2021, November 21). Wikipedia. https://en.wikipedia.org/wiki/Lens#Uses
Mirror. (2022, January 11). Wikipedia. https://en.wikipedia.org/wiki/Mirror#Physical_principles

Physics Tutorial: Refraction and the Ray Model of Light. (2020). Physicsclassroom.com. https://
www.physicsclassroom.com/class/refrn/Lesson-5/The-Mathematics-of-Lenses
Priyanshi. (n.d.). Di
ff
erence Between Mirror and Lens with its Practical Applications in Real Life.
BYJUS. https://byjus.com/physics/di
ff
erence-between-mirror-and-lens/
The Anatomy of a Lens. (2019). Physicsclassroom.com. https://www.physicsclassroom.com/class/
refrn/Lesson-5/The-Anatomy-of-a-Lens

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