optics

mirrors lenses

Compound/ thick lenses

Lens-makers’ eq’n

Ref raction at spherical

surf ace

Plane/ convex/ concave

Thin lenses

Real/ Virtual images

systems

aberrations

Camera/ eye/magnifier/

microscope/ telescope

Ray tracing

• Real/virtual images

• Upright/inverted

• q: image distance, p: object distance

• Magnification: M = -q/p

• For mirrors: f = R/2

To recap:To recap:

Paraxial rays

f = R/2

principal axis

centre of curvature R

Mirror equationMirror equation

Orange triangle similar to green triangle

o o

i i

h d ph d q

1o o

i

h d f ph f f

Combining …

1

1 1 1

1 1 1

p pq f

q f p

p q f

Mirror equation f = R/2

Sign Conventions for MirrorsSign Conventions for Mirrorsp > 0 if object is in front of the mirror (real object)p < 0 if object is in back of mirror (virtual object)

q > 0 if image is in front of mirror (real image)q < 0 if image is in back of mirror (virtual image)

If M > 0 image is uprightIf M < 0 image is inverted

Both f and R > 0 if centre of curvature is in front of mirror (concave mirror)Both f and R < 0 if centre of curvature is in back of mirror (convex mirror)

Ray tracingRay tracing

Three situations for spherical mirrors:

Concave: p > f Concave: p < f

Convex: p anywhere

Concave mirror: p > f

5 cm

20 cm

1 1 1

1 1 1 1 1 4 1 35 20 20 20

20 cm

3

f

p

p q f

q f p

q

20 / 3 1

20 3

qM

p

Concave: p < f

10 cm

6 cm

1 1 1

1 1 1 1 1 3 5 210 6 30 30

15 cm

f

p

p q f

q f p

q

15 56 2

qM

p

Convex mirror

15 cm

10 cm

105 cm

2 21 1 1

1 1 1 1 1 3 1 45 15 15 15

15 cm

4

p

R

Rf

p q f

q f p

q

15/ 4 115 4

qM

p

mirrors.html

Spherical Mirrors

1 1 1p q f

qM

p

sign conventions

concave: p > f real

concave: p < f virtual

convex virtual

2000 Q6

a) Draw a ray diagram showing the formation of a magnified image in a concave spherical mirror.

b) A shaving or make-up mirror of this type has a radius of curvature of 30 cm. What is the magnification of the image when the face is 10 cm from the centre of the mirror?

A 1-cm high object is positioned 12 cm in A 1-cm high object is positioned 12 cm in front of a spherical concave mirror having front of a spherical concave mirror having a radius of curvature of 8 cm. Completely a radius of curvature of 8 cm. Completely describe the resulting image.describe the resulting image.

Design a spherical mirror which will form an upright half-sized image of an object if thatobject is 100 cm from the vertex. Wherewill the image be located?

A concave spherical mirror of 20-cm radius isto be used to project an image of a candleonto a wall 110 cm away. Where will thecandle have to be placed and what will theimage look like?