Lecture 14 Mirrors by HC12031920163

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									              Lecture 14
               Mirrors
             Chapter 23.1  23.3


                  Outline

• Flat Mirrors
• Spherical Concave Mirrors
• Spherical Convex Mirrors
                    Flat Mirrors
                                          p       q
Source of light is placed at point
O at a distance p from a flat
mirror.
Point I is the image of point O.
q is the image distance.

Image is formed at the ray
intersection point, either real
or apparent.
Images seen in flat mirrors are always virtual images.
           Images in Flat Mirrors
To find out where an image is
formed, follow at least two
rays reflected from the mirror.

Triangles PQR and P′QR are
identical  PQ = P′Q

 The distance between the image and the mirror is
 the same as the distance between the object and the
 mirror, but they are located at different sides of the
 mirror.
               Magnification
Lateral magnification M is defined as follows:

               image height h′
           M ≡  = 
               object height h

M = 1 for flat mirrors.
The image in a flat mirror is unmagnified, virtual,
and upright and have an apparent left-right
reversal.
              Spherical Mirrors
A spherical mirror is a reflecting segment of a sphere.
A concave mirror is a spherical mirror with a
reflecting inner, concave surface.
            Spherical Mirrors
The image I of the object O
is real.
The image is sharp when
the diverging rays from the
object make small angles
with the principal axis.
When these angles are large,
the reflected rays intersect at   This phenomenon
different points and form a       is called spherical
blurry image.                     aberration.
      Image Formation in Concave
               Mirrors
tan  = h/p = h'/q

M = h'/h = q/p

tan  = h/(pR)
tan  = h'/(Rq)


h' Rq   q                1 1 2
                         +=   Mirror
 =  = 
                          p q R   equation
h   pR p
       Images in Concave Mirrors
When the object is far away from the mirror, the
image point is roughly halfway between the center
of curvature and the center of the mirror.
In this case incoming rays are nearly parallel to each
other,
the image point is called the focal point, and
the image distance is called the focal length (f = R/2).
                      1     1 1
                      +=
                      p     q f
Image Types
   A real image is formed when
   light rays pass through and
   diverge from the image point.


    A virtual image is formed
    when light rays do not pass
    through the image point but
    appear to diverge from that
    point.
              Convex Mirrors
1 1 2
+=
p q R
1  1 2
=+
q  p R

R =  70 cm    q = 20.4 cm     M = p/q = 0.417

  Problem: a candle is 49 cm from a convex mirror
  of 70 cm radius.
  Find the image distance and magnification.
Sign Convention
                    Summary
• Flat mirrors form virtual and unmagnified images.
• Spherical mirrors form both real and virtual images.
• Focal point of a spherical mirror is a point where
  parallel incoming rays intersect after reflection.
• The mirror equation connects the object distance,
  the image distance, the radius of the mirror
  curvature.

								
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