Chapter 17 Reflection and Mirrors | Sean
Plane Mirrors 17.1
Introduction
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Reflection is the change in direction of an
electromagnetic wave (in light) at a surface
that causes it to move away from it.
Incident ray is the ray hitting the surface.
Angle of incidence is the angle between the
normal and incident ray. 𝜃𝑖
Reflected ray is the ray leaving the surface.
𝜃𝑟
Law of reflection states that; "the angle of
incidence is always equal to the angle of
reflection." 𝜃𝑖 = 𝜃𝑟.
Normal
Incident ray
Reflected ray
Θi
Θr
Flat surface
Θi=Θr (Law of reflection)
Figure 1
Specular and diffuse reflection
Specular reflection
Light reflected from smooth, shiny
surfaces (i.e., mirrors or still water) is
reflected in only one direction.
Θi
Diffuse reflection
Light reflects from rough, dull (textured
surfaces) such as paper, clothes, or
unpolished wood in many directions.
Θi
Θr
Θr
Smooth surface
Figure 2
Different normal
Law of reflection
The law of reflection applies to both
smooth and rough surfaces (𝜃𝑖 = 𝜃𝑟).
However, the normal to the surface
location the ray strikes are not parallel.1
Rough surfaces prevent parallel
reflection and instead scatter it in
different directions.
Rough surface
Figure 3
1
The law of reflection still applies even when the normal is not parallel to the surface at which it
strikes. Refer to Figure 3.
pg. 1
Chapter 17 Reflection and Mirrors | Sean
Objects and plane mirror images
Keywords
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Plane mirror is a flat, smooth surface from which light is reflected by specular
reflection.
Object is either a luminous source of light rays or is illuminated via a source of light.
Virtual image is an image formed by diverging light rays.
○ Image is always on the opposite side of the mirror.
○ It is called a virtual image because there are no light rays present at the
image location.
Virtual image properties
1. Image appears to be the same distance behind the mirror. 𝑋𝑜 = 𝑋𝑖.
2. Image appears to be the same shape and size. 𝐻𝑜 = 𝐻𝑖.
3. Image is vertically oriented as the object is upside right. (As opposed to upside
down.)
4. Image form is laterally inverted. (Left is right, right is left.)
Steps to draw the image formed
1. Choose a point on the object, then draw a ray from the point to the mirror in different
directions.
2. Reflect the rays off the mirror. 𝜃𝑖 = 𝜃𝑟.
3. Trace the reflected rays back into the mirror and find intersections.
4. Repeat for other points.23
2
These steps differ depending on the type of mirror and can be considered as rough instruction and
inexact.
3 If he asks for steps in a test, note these down. ~ Sean
pg. 2
Chapter 17 Reflection and Mirrors | Sean
Curved and convex mirrors 17.2
Introduction
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Principal axis is the straight line (that includes the line segment). Perpendicular to the
mirror’s surface dividing it in two halves.
Focal point is a point at which incident light rays parallel to the principal axis
converge after reflecting from a mirror.
Convex
mirror
Concave
mirror
C
F
M
M
F
C
Figure 4
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The distance between F and M is half the distance between CM. 𝑟 = 2𝑓.
Focal length is the distance between the mirror and the focal point and can be
𝑟
expressed as 𝑓 = 2.
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Radius of curvature (r) is twice the length of the focal length.
Concave mirrors
Concave mirrors have inwardly curving reflection surfaces.
● Edges curve towards the observer.
● Reflected rays intersect the principal axis at point (f) and can be focused.
● The focal length is positive.
Convex mirrors
Convex mirrors have outwardly curving reflection surfaces with the edges that curve away
from the observer.
● The focal length is negative.
pg. 3
Chapter 17 Reflection and Mirrors | Sean
Other keywords
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Real image is the image formed by converging light rays that invert the image. The
image can be projected.
Magnification (m) is the image’s height divided by the object’s height, equal to the
negative image position divided by the object’s position.
ℎ𝑖
𝑥𝑖
○
𝑚 = ℎ𝑜 = − 𝑥𝑜
○
ℎ𝑖 = −
○
If |m| >1 the image is enlarged, |m|<1 the image is belittled, diminished.
■ The sign of magnification tells if the image is upright or inverted, so an
upright-virtual image has an |m| +ve, and (xi) -ve.
𝑥𝑖⋅ℎ𝑜
𝑥𝑜
Examples of concave mirrors
1
2
Object
F
Object
F
C
C
Real Image
Concave
Mirror
Concave
Mirror
Real Image
Figure 5
Figure 6
3
F
C
Virtual Image
Object
1.
(Figure 5) The image is
real, minimized, inverted and
between the object and focal
point.
2.
(Figure 6) The image is
real, magnified, inverted, and
further away from ‘c.’
3.
(Figure 7) The image is
virtual, upright, and magnified.
Concave
Mirror
Figure 7
pg. 4
Chapter 17 Reflection and Mirrors | Sean
Ray diagram
A Ray diagram is a visual representation of the image formed, depending on where the
object is placed with relation to focal point.
1
2
Object
Convex Mirror
Virtual
Image
Focal Point
Figure 8
1. Draw a line parallel to the principal axis and use F (Focal point) to guide the reflected
ray.
2. Draw a ray directed towards F and reflect it back. (Parallel).
○ Since there is no intersection between the reflected rays; No real image is
formed.
○ Tracing back reflected rays intersected between mirror and F.
■ Therefore, a virtual, upright, and minimized image is formed.
○ Convex mirrors always create virtual images.
Mirror Equations
1
𝑓
=
1
𝑥𝑖
+
1
𝑥𝑜
The reciprocal of the focal length of spherical mirrors is equal to the sum of the
reciprocal of the image and object’s position.4
𝑥𝑖 =
𝑓⋅𝑥𝑜
𝑥𝑜−𝑓
, 𝑥𝑜 =
𝑓⋅𝑥𝑖
𝑥𝑖−𝑓
,𝑓=
𝑥𝑖⋅𝑥𝑜
𝑥𝑖+𝑥𝑜
Virtual image
For an image to be “virtual,” its ‘xi’ must be -ve.
In the case of concave mirrors if the object is between ‘f’ and the mirror, the image
produced is virtual.
As for convex mirrors, the image produced is always virtual.
4
Wherein ‘f’ is the focal length, ‘xi’ is the image position, and ‘xo’ is the object position.
pg. 5