Reflections in Curved Mirrors (old version)

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.

Convex & Concave Mirrors

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

TerminologyCenter 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

TerminologyNormal

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

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 vertexNote: the distance from C to the vertex is 2f

Terminology

principal axis

vertex

fC

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

1)A light ray parallel to the principal axis is reflected through F

C Fh

C Fh

C Fh

C Fh

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

2) A light ray through F will reflect parallel to the principle axis

C Fh

C Fh

C Fh

C Fh

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

3) A light ray through C is reflected back onto itself

C Fh

C Fh

C Fh

C Fh

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

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

4) A light ray aimed at the vertex will follow the Law of Reflection (angle of incidence = angle of reflection)

C Fh

C Fh

C Fh

C Fh

LOCATING AN IMAGE ON 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 ON A CONCAVE MIRROR

Ray 1 - travels parallel to the principal axis and reflects through the focal point (F)

LOCATING AN IMAGE ON A CONCAVE MIRROR

Ray 2 - travels through the focal point and reflects parallel to the principal axis

LOCATING AN IMAGE ON A CONCAVE MIRROR

The point where the two reflected rays converge will be the location of the image

LOCATING AN IMAGE ON A CONCAVE MIRROR5 Situations1. 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

Size Attitude Location Type

Reduced

Inverted Between C & F

Real

Case 2

Size Attitude Location Type

Same Inverted At C Real

Case 3

Size Attitude Location Type

Enlarged

Inverted Beyond C

Real

Case 4

Size Attitude Location Type

No Image Formed!

Case 5

Size Attitude Location Type

Enlarged

Upright Behind mirror

Virtual

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

1)A ray parallel to the principal axis is reflected as if it had come through F

F C

h

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

2) A ray aimed at F is reflected parallel to the principal axis

F C

h

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

3) A ray aimed at C is reflected back upon itself

F C

h

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

4) A light ray aimed at the vertex will follow the Law of Reflection

F C

h

LOCATING AN IMAGE ON 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 ON A CONVEX MIRROR

Ray 1: travels parallel to the principal axis and reflects through the focal point

BEFORE AFTER

LOCATING AN IMAGE ON A CONVEX MIRROR

Ray 2: travels towards the focal point and reflects parallel to the principal axis

BEFORE AFTER

LOCATING AN IMAGE ON A CONVEX MIRROR

The image appears where the (virtual) reflected rays appear to intersect

Remember:

The image for a convex mirror is always virtual, upright and

smaller!

Try it!