optics m irrors lenses Com pound/ thick lenses Lens-m akers’ eq’n Refraction at spherical surface Plane/ convex/ concave Thin lenses Real/ Virtual images system s aberrations Cam era/eye/ magnifier/ m icroscope/ telescope Ray tracing
Jan 13, 2016
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?