# 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
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