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.