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Mirrors and Lenses
• How do eyeglasses correct your vision?
• When you look in a mirror, where is the face you
see?
• In which ways is a cell phone camera similar to a
human eye?
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Plane mirrors
• The simplest mirror is a plane mirror—a flat,
reflective surface, often consisting of a metal film
covered in glass.
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Seeing light from an object
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Plane mirrors
• The image of the real object seen in the mirror is
located where light reflected from the mirror to
the eye of the observer seems to originate.
– This perceived image is behind the mirror and
not on the surface of the mirror.
• Using the ray diagram, we find that the image is
exactly the same distance behind the plane
mirror as the object is in front of it.
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Plane mirror virtual image
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Qualitative analysis of curved mirrors
• A curved mirror is cut from a spherically shaped
piece of glass backed by a metal film.
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Concave mirrors
• Concave mirrors are often used for
magnification, in both telescopes and cosmetic
mirrors.
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Convex mirrors
• Convex mirrors are used as passenger- side
rearview mirrors and to provide visibility at blind
spots, such as hallway corners and driveway
exits.
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Concave mirrors
• Concave mirrors cause parallel incident rays to
pass through a single point after reflection.
– If the incident rays are also parallel to the
principal axis, this point is called the focal
point F of the mirror.
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Tip
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Focal point of a concave mirror
• If a mirror has a large radius of curvature
compared to its size and the incident rays are
close to the principal axis, the focal point is
approximately halfway between the center of the
mirror and the center of curvature.
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Reasoning Skill: Constructing a ray diagram
to locate the image of an object produced
by a concave mirror
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Tip
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Creating a virtual image with a concave
mirror
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Locating the image of the base of an object
produced by a concave mirror
• The image of the base of the object is always on
the principal axis directly below the image of the
top of the object.
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Convex mirrors
• With a convex mirror, rays parallel to the
principal axis diverge after reflection from the
virtual focal point F behind the mirror.
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Reasoning Skill: Constructing a ray diagram
to locate the image produced by a convex
mirror
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The mirror equation
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Tip
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Objects far away from the mirror
• If an object is extremely far away along the
principal axis, we can assume that rays from the
object reaching the mirror are parallel to the
principal axis.
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Mirror equation
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Magnification
• The change in the size of the image compared to the size
of the object is a quantity called linear magnification m:
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Linear magnification
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Tip
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Qualitative analysis of lenses
• A lens is a piece of glass or other transparent
material with two curved surfaces that produces
images of objects by changing the direction of
light through refraction.
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Convex lenses
• A convex lens made of
glass is similar to a
concave mirror where
incident rays parallel to
the principal axis intersect
at a focal point after
passing through the lens.
– How the rays converge
depends on the
curvature of the surface
of the lens.
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Tip
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Convex lenses with water
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Reasoning Skill: Constructing ray diagrams
for single-lens situations: Convex lens
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Reasoning Skill: Constructing ray diagrams
for single-lens situations: Concave lens
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Concave lenses
• For concave lenses, light seems to diverge from
a single point on the axis—the virtual focal point.
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Ray diagrams for various lenses
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Ray diagrams for various lenses
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Image location of the base of the object
• The image of the base of the object is directly
beneath on the principal axis.
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Thin lens equation and quantitative analysis
of lenses
• A thin lens has a radii of curvature much larger
than the size of the lens.
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Thin lenses
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Tip
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Seeing a sharp image on a screen
• A screen must be placed
where the image is located
to view a sharp image.
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Tip
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Linear magnification in lenses
• Lenses can produce images that are larger or
smaller in size than the original objects.
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Skills for analyzing processes involving
mirrors and lenses
• When problem solving:
– Assume the lens/mirror is only slightly curved
and the rays are incident near the principal
axis.
– Draw a ray diagram representing the situation
in the problem.
– Use the picture and ray diagram to help
construct a mathematical description of the
situation.
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Photography and cameras
• Light from an object enters the camera through
the lens, which focuses the light on a surface
that has light-sensitive properties (an image
sensor).
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Light field photography
• In light field photography, the image sensor records all
the light entering the camera, not just the light that would
produce a sharp image on the focal plane.
– A photographer can choose an object to focus on
after the picture has been taken, because the camera
effectively focuses on all objects at once.
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Optics of the human eye
• Light from an object enters the cornea and passes
through a transparent lens.
• An iris in front of the lens widens or narrows, like the
aperture on a camera that regulates the amount of light
entering the device.
• The retina plays the role of the film.
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Optics of the human eye
• When the eye looks at
distant objects, muscles
around the lens of the
eye relax, and the lens
becomes less curved.
• As the object moves
closer, the eye muscles
contract, increasing the
curvature of the lens
and reducing the focal
length.
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Corrective lenses
• The two most common
vision abnormalities
corrected with lenses are
myopia (nearsightedness)
and hyperopia
(farsightedness).
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Corrective lenses (Cont'd)
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Tip
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Angular magnification and magnifying
glasses
• The impression of an object's size is quantified
by its angular size:
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Angular magnification
• The angular magnification M of an optical
system is defined as:
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Angular size of the object as seen with the
unaided eye
• The maximum angular size
of an object viewed by the
unaided eye is:
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Finding the image produced by multiple
lenses
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Telescopes
• A common telescope
has two convex
lenses separated by
a distance slightly
less than the sum of
their focal lengths.
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The compound microscope
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Summary
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Summary
© 2014 Pearson Education, Inc.
Summary
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Summary
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