Chapter 36. Image Formation
36.1 Images Formed by Flat Mirrors
p:
q:
O:
I:
object distance
image distance
object
image
(1) Type of image
Real image is one in
which rays converge
at the image point.
Virtual image is one in which the light ray do not converge
to the image point but appear to emanate from that
point.
The images seen in flat mirror are always virtual.
(2) Location of image
To find out where the
image is formed, follow at
least two rays of light as
they reflect from the
mirror.
The image is as far behind the mirror as the object is in
front (p = q). The image is upright.
(3) Lateral magnification M
image height h'
M
=
Define
object height h
For flat mirror, M = 1. The image is unmagnified.
Q: How tall the mirror
needs to be in order to view
the whole body.
36.2 Images Formed by Spherical Mirrors
Concave Mirrors
Reflection Characteristics:
(1) Any light ray passing through the center of curvature, C,
will be reflected back on itself.
(2) A point object O placed on the principle axis that is farther
than R from the mirror surface, forms a real image at I.
(3) Light ray from a distant object reflected from a concave
mirror will go through the focal
point, F.
Focal length
f = R/2
Image formation:
Let p be the object distance, and q be the image distance.
(1) If p > R, the image is real, inverted, and reduced in size.
(2) If p < R/2, the image is virtual, upright, and enlarged.
Mirror equation
Magnification
1 1 1
+ =
p q f
h'
q
M= =
h
p
Example A concave mirror has a focal length of 10 cm. Find
the location of the image for object distances of (a) 25 cm,
(b) 10 cm, and (c) 5 cm.
Solution
f = 10 cm, R = 2f =20 cm.
(a) p = 25 cm. Thus p > R.
The image is real, inverted, and reduced in size.
1
1
1 1 1
1
q = 16.7 cm
+ =
+ =
p q f
25cm q 10cm
q
16.7cm
M= =
= 0.668 (negative means inverted)
p
25cm
(b) p = 10 cm
The object is located at the focal point. The reflected rays
travel parallel to the principal axis. No image form.
1
1
1 1 1
1
q=
+ =
+ =
p q f
10cm q 10cm
(c) p = 5 cm, p < R
The image is virtual, upright, and enlarged.
1 1 1
1
1
1
q = -10 cm
+ =
+ =
p q f
5cm q 10cm
(negative: image is behind the mirror and is virtual)
q
(10cm)
M= =
=2
p
5cm
Convex mirror
• The image formed by the real object is virtual and upright.
• Equations for concave mirror also can be applied for convex
mirror with following sign convention:
Sign Convention for Mirrors
q > 0 if the image is in front of the mirror (real image).
q < 0 if the image is in back of the mirror (virtual image).
Both f and R > 0 for concave mirror.
Both f and R < 0 for convex mirror.
M > 0, the image is upright.
M < 0, the image is inverted.
Example: An object 3 cm high is placed 20 cm from a convex
mirror with focal length of 8 cm.
(1) Find the position of the image.
Convex mirror: R and f are negative. Thus f = -8 cm.
1
1
1 1 1
1
+ =
+
=
q p f
q 20cm 8cm
q = -5.71 cm (a virtual image behind the mirror)
(2) Find the magnification:
5.71cm q
M = = = 0.286
20cm p
The image is upright and reduced in size.
36.3 Images formed by Refraction
Paraxial rays: light rays that diverge from the object make a
small angle with the principal axis.
n1 n2 n2 n1
+ =
p q
R
Sign Convention for Spherical Refraction Surface and thin
lenses:
P > 0, if the object is in front of the surface (real image)
P < 0, if the object is in back of the surface (virtual image)
q > 0 if the image is in back of the surface (real image).
q < 0 if the image is in front of the surface (virtual image).
R > 0 if the center of curvature is in back of surface.
R < 0 if the center of curvature is in front of surface.
M > 0, the image is upright.
M < 0, the image is inverted.
Example: A coin 2 cm in diameter is embedded in a solid glass
ball of radius 30 cm. The index of refraction of the ball is n1 =
1.5, and the coin is 20 cm from the surface. Find the position of
the image.
Solution:
n1 n2 n2 n1
+ =
p q
R
1 1 1.5
1.5
+ =
20cm q 30cm
q = -17.1 cm
The image is formed in the
glass and is virtual.
Flat Refracting Surfaces
If the refracting surface is flat,
R
n
n
n1
q= 2 p
= 2
n1
p
q
The image formed by a flat
refracting surface is on the same
side of the surface as the object
(virtual, upright image).