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Lecture today: Chapter 34 Images
1) Reflection by flat (plane) mirror
2) Reflection by spherical mirrors
Announcements:
- Exam 2 Wednesday October 29
In chapter 34 we will describe how
- reflection by light by mirrors
- refraction of light by lenses
can create images
image (a reproduction derived from light) of an object
Application: glasses, projector, telescope, microscope, mirrors
Examples of this, you already know:
Reflection by a flat mirror
For example, if the light rays have been reflected toward you from a standard flat mirror,
the image of a friend (or oneself) appears to be behind the mirror because the rays you
intercept come from that direction. Of course, your fiend is not back there. This type of
image, which is called a virtual image, truly exists only within the brain but nevertheless
is said to exist at the perceived location.
A real image differs in that it can be formed on a surface, such as a card or a movie
screen. You can see a real image
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In this chapter we explore several ways in which virtual and real images are formed by
reflection (as with mirrors) and refraction (as with lenses).
Flat (Plane) Mirrors: Flat reflecting surface
θ
θ
Incident angle θ is the same as
reflected angle.
O
I
Person = object, O
Image = I
Equation relating image distance (i) to object distance (p) for a flat mirror:
i = -p
(plane mirror)
By convention
object distances p are taken to be positive quantities
image distances i negative quantity because flat mirror produces a virtual image
Spherical mirrors:
We turn now from images produced by plane mirrors to images produced by mirrors with
curved surfaces. In particular, we consider spherical mirrors, which are simply mirrors in
the shape of a small section of the surface of a sphere. A plane mirror is in fact a
spherical mirror with an infinitely large radius of curvature and thus an approximately
flat surface.
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Lecture 18/Page 3
i) Concave mirror (mirror surface is caved in)
Curving the surface in this way changes several characteristics of the mirror and the
image it produces of the object
C = the center of curvature of the mirror
F = focal point (or focus) of the mirror
r = radius of curvature of mirror
f = focal length of mirror
Rays that are parallel to the mirrors central axis will all go through the focus (converge at
F).
ii) Convex mirror (mirror surface flexed out)
In a convex mirror, incident parallel light rays seem to diverge from a virtual focus at F,
on the side of the mirror opposite the light rays.
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DEMO: mirage
Two concealed, opposing parabolic mirrors. The physical object to be converted to a
hologram is placed in the concave center of the bottom mirror. A hologram instantly
projects up through this aperture, appearing to the viewer as a truly solid object.
Hence, from the Demo we can see that mirrors can produce real images.
Let’s consider the following 4 cases for convex/concave mirrors.
i) Concave mirror, p<f (object O inside the focal point of a concave mirror)
virtual, upright image
ii) Concave mirror, p=f (object O at focal point of a concave mirror)
no image
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iii) Concave mirror, p>f (object O between focal point and C of a concave mirror)
real, inverted image
iv) Convex mirror,
virtual, upright image
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Locating Images by Drawing Rays (Ray tracing diagrams)
We can graphically locate the image of any off-axis point of the object by drawing a ray
diagram with any two of four special rays through the point:
1. A ray that is initially parallel to the central axis reflects through the focal point F
2. A ray that reflects from the mirror after passing through the focal point emerges
parallel to the central axis.
3. A ray that reflects from the mirror after passing through the center of curvature C
returns along itself.
4. A ray that reflects from the mirror at point c is reflected symmetrically about that axis
The image of the point is at the intersection of the two special rays you choose.
The image of the object can then be found by locating the images of two or more of its
off-axis points. You need to modify the descriptions of the rays slightly to apply them to
convex mirrors.