Reflection at Mirrors and
Curved Surfaces
Amy C Nau, OD
Regular (specular) reflection

Reflected light leaves the surface in
definite beams that follows the laws of
reflection. Occurs at smooth surfaces.
Think of throwing a ball against a wall, or playing pool
Specular Reflection
http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l1d.html
Reflection at Plane Surface
N
The incident angle determines the final direction of the ball
Incident and emergent angles are measured from a perpendicular
line (normal) to the surface (interface).
Law of Reflection
Incident
ray
Normal
Incident angle
Reflected angle
Reflected
ray
Medium 1 (n)
interface
qi
qr
Medium 2 (n’)
The angle of incidence is equal to the angle of reflection qi=qr
Law of Plane Mirrors

the states that "the image is always the same distance behind the
mirror as the object is in front of the mirror."
eye

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Rays entering the eye are diverged from the mirror's surface. Since the eye
has to "dot back" the rays to form an image, this image is virtual The image
is upright, but left-right reversed
Distance of the image = distance of the object
Mirrors

Obey the Law of Reflection: the angle of incidence equals the
angle of reflection
Note that these angles are measured from the normal to either the
incident or reflected rays.
Mirrors
The following diagram illustrates that the minimum length of a plane mirror required
for someone to view their entire image equals half their height.
http://dev.physicslab.org/Document.aspx?doctype=3&filename=GeometricOptics_PlaneMirrors.xml
Mirrors


the magnification of a plane mirror equals one. Size of image = size
of object
Recall that magnification is calculated using the formula:
Reflection at a Plane Mirror
Incident ray
Reflected ray
Real space
Real object
Real image
Reflecting surface
Virtual space
Virutal object
Virtual image
Reflection at plane mirror

Law of reflection states that incident and
reflected angles are equal. Opposite
internal angles aremirror
also equal
Virtual, erect image
Real object
l
l’
l=-l’
Reflection Basics


Rays leaving the surface diverge as though they
came from the image position
The image is virtual, erect and equal

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An image, although reversed, will have the same size
and orientation as the object
The image distance is equal in magnitude to the
object distance (but opposite in sign)

If you stand 1m in front of a mirror, you will see your
image 1 m behind the mirror
Deviation of Rays at Reflecting
Surface
qr
90-qr
90-qi
Plane Mirrors
the image produced is upright
the image is the same size as the object
the image distance = the object distance
the image is a virtual image
Spherical Mirrors
They are either convex (reflective surface outside a sphere)
Or they are concave (reflective surface inside a sphere)
You may easily experience this by looking into a serving spoon
If convex, your image is virtual, upright and reduced
in size. Covnex mirrors are considered to be negative mirrors
If concave, your image can be real or virtual depending
On where the object is located relative to the focal point.
Convex Mirror
Shiny surface is the front of the mirror.
The radius is behind the mirror and is represented
By the line VC where V is the vertex of our convex mirror and C is the center of a ball.
The focal length, f, is half of the radius, or the length of the line VF. F is called the focal point.
Ray Diagrams
All three reflected rays diverge. Their "dotted back reflections" always
form virtual, upright, reduced images located between V and F.
Concave Mirror
If the light rays, once reflected off the mirror, converge back together,
then the image will be real. It is called a real image because the actual,
real, rays of light form the image.
Real images have the property that they are always
inverted and left-right reversed
Concave Mirror
object located infinitely far away
http://dev.physicslab.org/Document.aspx?doctype=3&filename=GeometricOptics_SphericalMirrors.xml
Concave Mirror
located in region 1
object is located in region II
Concave mirror summary
any object beyond C will have an image that is
real, inverted compared to the object, and
between F and C.
 any object placed between F and C will have an
image that is real, inverted, and beyond C.
 when the object is between F and the mirror
the image will be behind the mirror, making it a
virtual image, and it will be upright compared to
the object.

Magnification
Convex mirrors = minification;
Concave mirrors = magnification

http://www.wfu.edu/physics/demolabs/dem
os/avimov/bychptr/chptr9_optics.htm
Curved Surfaces
Object Space
Index before refraction (or reflection) n
Real objects
Virtual images
Image Space
Index post refraction or reflection n’
Real images
Virtual objects
+ direction of light
Negative measurements
Positive measurements
Curved Surfaces
Real object- object that emits divergent
wavefronts. Radius and vergence are
negative, Real objects must be to the left
of the interface
 Real Image- image formed with
convergent wavefronts, which have
positive values. Located at the right of the
interface and can be formed on a screen

Curved Surfaces

Virtual object- when convergent wavefront is
obstructed by an obstacle (i.e. refracting
surface) the position to which the wavefront is
headed is the virtual object position. To the right
of the interface

Virtual image- when divergent wavefront leaves
a refracting surface, the center of curvature of
the wavefront is the virtual image position.
Located to the left of the interface
Curved Surfaces

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Gaussian Imaging Equation: Used to calculate
object position, image position and power.
A refracting surface changes the vergence of
light incident upon it. The amount of change is
equal to the power of the surface
L’=L+F
L’=emerging vergence after refract
L= incident vergence
F= power of the surface
Curved Refracting Surfaces
Any point on a curved surface reflects light
according to Snell’s law.
 The shape of the surface will determine
the size, position, type and quality of the
resulting image
 Spheres are used for Rx lenses, contacts,
IOL’s, instruments
 We will only consider one surface for
simplicity

Curved Surfaces- some concepts

Spherical surface is defined by the radius,
curvature or power
Radius- distance from arc to any point
 Curvature- reciprocal of radius
 Center of curvature - equidistant form any
point on surface
 Sag- perpendicular distance from chord to
surface
 Chord- straight line connecting any two points
on any arc

Curved Surfaces
Center of curvature
radius
sag
chord
Contact lens formula for sag depth
r=y2/2s+s/2
Radius-Power Relationship
F=n’-n/r
 Clinically, this is commonly used to convert
K readings to radius readings.
 This is also the premise of a “lens clock”,
which is used to measure lens power
 Power is + when wavelength converges
and - for diverging wavelengths.

Curved Mirrors

F=n’-n holds, but since n’=n for mirrors,
the formula can be rewritten as F=-2n/r
Multiple Images

Two mirrors facing each other form
multiple (infinite) images of the object
placed between them