PHYS120
Spherical mirrors
Department of Physics
School of Chemistry & Physics
University of kwaZulu-Natal
11/09/2018 – Lecture 3
PHYS120 Geometrical Optics
Definitions
A
P C
X b
Y
C - centre of curvature
P - pole
PC - radius of curvature
XY - principal axis
AB - aperture
PHYS120 Geometrical Optics
Action on parallel light
For a spherical mirror with large radius of curvature and rays
close to the principal axis, AF ≈ PF. Hence f = 12 r .
α
A α
2α α
P F C
PHYS120 Geometrical Optics
Spherical aberration
Spherical aberration: A wide A parabolic mirror brings all
beam shows distortion after parallel incoming rays to a point
reflection from a spherical mirror. focus.
PHYS120 Geometrical Optics
Concave mirror (object outside F)
object
F
b
PHYS120 Geometrical Optics
Concave mirror (object outside F)
object
F
b
Ray parallel to axis is reflected through F.
PHYS120 Geometrical Optics
Concave mirror (object outside F)
object
F
b
Ray parallel to axis is reflected through F.
Ray through F is reflected parallel to axis.
PHYS120 Geometrical Optics
Concave mirror (object outside F)
object
F
b
Ray parallel to axis is reflected through F.
Ray through F is reflected parallel to axis.
Ray through pole is reflected symmetrically.
PHYS120 Geometrical Optics
Concave mirror (object outside F)
object
F
b
image
Ray parallel to axis is reflected through F.
Ray through F is reflected parallel to axis.
Ray through pole is reflected symmetrically.
PHYS120 Geometrical Optics
Concave mirror
For an object outside F, the image is always ‘real’ and ‘inverted’.
PHYS120 Geometrical Optics
Concave mirror
For an object outside F, the image is always ‘real’ and ‘inverted’.
When the object is outside C, the image is diminished.
PHYS120 Geometrical Optics
Concave mirror
For an object outside F, the image is always ‘real’ and ‘inverted’.
When the object is outside C, the image is diminished.
When the object is at C, so is the image and they are the
same size.
PHYS120 Geometrical Optics
Concave mirror
For an object outside F, the image is always ‘real’ and ‘inverted’.
When the object is outside C, the image is diminished.
When the object is at C, so is the image and they are the
same size.
When the object is between C and F, the image is
enlarged.
PHYS120 Geometrical Optics
Concave mirror
For an object outside F, the image is always ‘real’ and ‘inverted’.
When the object is outside C, the image is diminished.
When the object is at C, so is the image and they are the
same size.
When the object is between C and F, the image is
enlarged.
When the object is at F, the image is at infinity (the
reflected rays are parallel).
PHYS120 Geometrical Optics
Concave mirror (object inside F)
F C
b b
PHYS120 Geometrical Optics
Concave mirror (object inside F)
F C
b b
Ray parallel to axis is reflected through F.
PHYS120 Geometrical Optics
Concave mirror (object inside F)
F C
b b
Ray parallel to axis is reflected through F.
Ray through C is reflected back along its own path.
PHYS120 Geometrical Optics
Concave mirror (object inside F)
F C
b b
Ray parallel to axis is reflected through F.
Ray through C is reflected back along its own path.
Ray through pole is reflected symmetrically.
PHYS120 Geometrical Optics
Concave mirror (object inside F)
A′
F C
b b
Ray parallel to axis is reflected through F.
Ray through C is reflected back along its own path.
Ray through pole is reflected symmetrically.
Image is always virtual, upright and magnified.
PHYS120 Geometrical Optics
Convex mirror
b b
C F
PHYS120 Geometrical Optics
Convex mirror
b b
C F
Ray parallel to axis is reflected through F.
PHYS120 Geometrical Optics
Convex mirror
b b
C F
Ray parallel to axis is reflected through F.
Ray through C is reflected back along its own path.
PHYS120 Geometrical Optics
Convex mirror
b b
C F
Ray parallel to axis is reflected through F.
Ray through C is reflected back along its own path.
Ray through pole is reflected symmetrically.
PHYS120 Geometrical Optics
Convex mirror
A′
b b
C F
Ray parallel to axis is reflected through F.
Ray through C is reflected back along its own path.
Ray through pole is reflected symmetrically.
Image is always virtual, upright and diminished.
PHYS120 Geometrical Optics
Mirror formula
A
θ
θ
β γ α
P b b b
I C O
γ =α+θ (exterior angle of △AOC)
PHYS120 Geometrical Optics
Mirror formula
A
θ
θ
β γ α
P b b b
I C O
γ = α + θ (exterior angle of △AOC)
β = α + 2θ (exterior angle of △AOI)
PHYS120 Geometrical Optics
Mirror formula
A
θ
θ
β γ α
P b b b
I C O
γ = α + θ (exterior angle of △AOC)
β = α + 2θ (exterior angle of △AOI)
Eliminate θ, then α + β = 2γ
PHYS120 Geometrical Optics
Mirror formula
A
θ
θ
β γ α
P b b b
I C O
γ = α + θ (exterior angle of △AOC)
β = α + 2θ (exterior angle of △AOI)
Eliminate θ, then α + β = 2γ
For paraxial rays:
AP AP AP
α ≈ tan α ≈ OP , β ≈ tan β ≈ IP , γ ≈ tan γ ≈ CP
PHYS120 Geometrical Optics
Mirror formula
A
θ
θ
β γ α
P b b b
I C O
γ = α + θ (exterior angle of △AOC)
β = α + 2θ (exterior angle of △AOI)
Eliminate θ, then α + β = 2γ
For paraxial rays:
AP AP AP
α ≈ tan α ≈ OP , β ≈ tan β ≈ IP , γ ≈ tan γ ≈ CP
AP AP 2AP 1 1 2
Hence OP + IP = CP =⇒ u + v = r
PHYS120 Geometrical Optics
Magnification
u
Magnification (use similar triangles)
image size i v
m= = =
object size o u
PHYS120 Geometrical Optics
