Curved MirrorsConcave Convex
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Curved Mirrors
Concave Convex
“converging” mirror “diverging” mirror
Convex & Concave Mirrors
Which part of this circle is showing a convex mirror?
Which part is a concave mirror? How did you know?
Hint: You must first identify where the light rays are coming from and thus locating the reflective surface.
Centre of sphere
Concave mirror Convex mirror
Concave mirrors are shaped like part of the inside of a sphere
Convex mirrors are shaped like part of the outside of a sphere
Convex & Concave Mirrors
Terminology
Center of Curvature (C)
the centre of the sphere whose surface forms the curved mirror
Principal Axis the straight line passing
through the centre of curvature to the mirror (radius of sphere)
Vertex (V) or Pole (P) the point where the
principal axis meets the mirror
Terminology
Normal the straight line joining any point on a
curved mirror with the centre of curvature Notice it is the same as the radius and
principle axis
principal axis
vertex
fC
Terminology
Focal Point or Focus (F) - where the light rays meet, located at half the distance between centre of curvature and mirror (1/2 radius)
Focal Length (f) - the distance from the focal point to the vertex
Note: the distance from C to the vertex is 2f
Concave Mirrors
Concave Mirrors
Surface of mirror is curved inwards forming a ‘cave’
Concentrates light rays Also known as converging mirror Produces a 3 different types of
images
Applications of Concave Mirrors
Applications of Concave Mirrors
Light Rays with Concave Mirrors1. A light ray parallel to the
principal axis is reflected through F
Notice how all the rays converge at F That’s why concave mirrors are also
known as converging mirrors
C Fh
C Fh
C Fh
C Fh
1. A light ray parallel to the principal axis is reflected through F
Light Rays with Concave Mirrors1. A light ray parallel to the
principal axis is reflected through F
2. A light ray through F will reflect parallel to the principle axis
Light Rays with Concave Mirrors2. A light ray through F will reflect
parallel to the principle axis Notice how all the rays reflect parallel
C Fh
C Fh
C Fh
C Fh
2. A light ray through F will reflect parallel to the principle axis
Light Rays with Concave Mirrors1. A light ray parallel to the
principal axis is reflected through F
2. A light ray through F will reflect parallel to the principle axis
3. A light ray through C is reflected back onto itself
Centre of curvature = centre of sphere
Light Rays with Concave Mirrors3. A light ray through C is
reflected back onto itself Why do rays that go through the centre
of curvature reflect back on itself?
Why do rays that go through the centre of curvature reflect back on itself? Any line through C is the same as the
…. of a circle The line through C has an angle of ….
relative to the mirror This line is also known as …. The angle of …. equals the angle of
incidence which explains why this line reflects back on itself
C Fh
C Fh
C Fh
C Fh
3. A light ray through C is reflected back onto itself
Light Rays with Concave Mirrors1. A light ray parallel to the
principal axis is reflected through F
2. A light ray through F will reflect parallel to the principle axis
3. A light ray through C is reflected back onto itself
4. A light ray aimed at the vertex will follow the Law of Reflection
C Fh
C Fh
C Fh
C Fh
4. A light ray aimed at the vertex will follow the Law of Reflection (angle of incidence = angle of reflection)
Locating an Image in a Concave Mirror
Any two light rays from the same location off an object is needed to locate its image
1. A light ray parallel to the principal axis is reflected through F
2. A light ray through F will reflect parallel to the principle axis
3. A light ray through C is reflected back onto itself
4. A light ray aimed at the vertex will follow the Law of Reflection
Locating an Image in a Concave Mirror
Ray 1 - travels parallel to the principal axis and reflects through the focal point (F)
Locating an Image in a Concave Mirror
Ray 2 - travels through the focal point and reflects parallel to the principal axis
Locating an Image in a Concave Mirror
The point where the two reflected rays converge will be the location of the image
Locating an Image in a Concave Mirror 5 regions where object could exist:
Locating an Image in a Concave Mirror5 regions where object could exist:1. Beyond C: Object is greater than 2 focal
lengths from the mirror (do>2f)2. At C: Object is at the centre of curvature
(do=2f)3. Between C and F: Object is between 1 and 2
focal lengths from the mirror (f<do<2f)4. At F: Object is at the focal point (do=f)5. Between F and mirror: Object is between
the mirror and the focal point (0<do<f)
Case 1 – Object Beyond C
Size Attitude Location Type
Reduced Inverted Between C & F
Real
Case 2 – Object at C
Size Attitude Location Type
Same Inverted At C Real
Case 3 – Object between C & F
Size Attitude Location Type
Enlarged
Inverted Beyond C
Real
Case 4 – Object at F
Size Attitude Location Type
No Image Formed!
Case 5 – Object between F & mirror
Size Attitude Location TypeEnlarged Upright Behind
mirrorVirtua
l
Convex Mirrors
Curved Mirrors
Concave Convex
“converging” mirror “diverging” mirror
Convex Mirrors
Surface of mirror is curved outward Spreads out light rays Also known as diverging mirror Produces a virtual image that is
upright and smaller than the object
Applications of Convex Mirrors
Light Rays with Convex Mirrors1. A ray parallel to the principal
axis is reflected as if it had come through F
Light Rays with Convex Mirrors1. A ray parallel to the principal
axis is reflected as if it had come through F
F C
h
1. A ray parallel to the principal axis is reflected as if it had come through F
Light Rays with Convex Mirrors1. A ray parallel to the principal
axis is reflected as if it had come through F
2. A ray aimed at F is reflected parallel to the principal axis
Light Rays with Convex Mirrors2. A ray aimed at F is reflected
parallel to the principal axis
F C
h
2. A ray aimed at F is reflected parallel to the principal axis
Light Rays with Convex Mirrors1. A ray parallel to the principal
axis is reflected as if it had come through F
2. A ray aimed at F is reflected parallel to the principal axis
3. A ray aimed at C is reflected back upon itself
F C
h
3. A ray aimed at C is reflected back upon itself
Light Rays with Convex Mirrors1. A ray parallel to the principal
axis is reflected as if it had come through F
2. A ray aimed at F is reflected parallel to the principal axis
3. A ray aimed at C is reflected back upon itself
4. A light ray aimed at the vertex will follow the Law of Reflection
F C
h
4. A light ray aimed at the vertex will follow the Law of Reflection
Locating an Image in a Convex Mirror
Any two light rays off the same location on the object are needed to locate an image
1. A ray parallel to the principal axis is reflected as if it had come through F
2. A ray aimed at F is reflected parallel to the principal axis
3. A ray aimed at C is reflected back upon itself
4. A light ray aimed at the vertex will follow the Law of Reflection
Locating an Image in a Convex Mirror
Ray 1: travels parallel to the principal axis and reflects through the focal point
BEFORE AFTER
Locating an Image in a Convex Mirror
Ray 2: travels towards the focal point and reflects parallel to the principal axis
BEFORE AFTER
Locating an Image in a Convex Mirror
The image appears where the (virtual) reflected rays appear to intersect
Locating an Image in a Convex Mirror
Size Attitude Location TypeReduced Upright Behind
mirrorVirtual
Try it!
Draw the light rays. Draw the image.
Locating an Image in a Curved Mirror1. Pick a point on the object (usually the top
of the object). 2. Send any two incident rays off the point on
the object (follow the light ray rules for curved mirrors choosing 2 of 4 possibilities).
3. Draw the reflected ray as a solid line (on the same side of the mirror as the object).
4. Find the intersection of the reflected rays. If the rays do not intersect, extend the reflected rays into the virtual side of the mirror (use dotted line) until they do.
5. Use the point of intersection to locate the image. Draw the image.
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