Corner Cube or Retro Reflectors
These Corner Cube or Retro Reflectors are resource
material to support parts of
STAO’s ScienceWorks
Grade 10 Optics
The following are excerpts from
L4 The Laws of Reflection (Slides 34 to 57 of 74)
Corner Cube or Retro Reflectors
Bicycle Reflectors
Corner Cube Reflectors,are
used in Bicycle Reflectors
When light is shone on them from something like a car
(Incident rays) it is reflected straight back toward
the car. The Reflected rays are parallel and in the
opposite direction of Incident rays.
Bicycle Reflectors
Why not just use a mirror
to reflect light back into
the Eye/Brain?
Bicycle Reflectors
Slight changes in the mirrors orientation would
cause the reflected light to miss the Eye/Brain?
Bicycle Reflectors
Slight changes in the mirrors orientation would
cause the reflected light to miss the Eye/Brain?
Bicycle Reflectors
If two mirrors are arranged at 90º, slight changes
in the mirrors orientation do not affect the
direction of the reflected light.
Bicycle Reflectors
If two mirrors are arranged at 90º, slight changes
in the mirrors orientation do not affect the
direction of the reflected light.
Bicycle Reflectors - Mathematical Proof
1) Use the laws of
reflection and
geometry to prove
light is reflected
back, parallel to the
incident ray from
two mirrors at right
angles?
Bicycle Reflectors - Mathematical Proof
At B, let the first
Angle of Incidence =
Angle of Reflection = x
or (i = r = x)
Bicycle Reflectors - Mathematical Proof
At C, let the second
Angle of Incidence =
Angle of Reflection = y
or (i = r = y)
Bicycle Reflectors - Mathematical Proof
Note A= 90º
In ∆ABC,
A+x+y = 180 º
90º+x+y = 180 º
 x+y = 90 º
The Transversal line BC
2x+2y = 2(x+y)
= 2(90º)
= 180º
Lines IB and CR
are parallel because the interior angles on the same
side of the transversal are supplementary
Bicycle Reflectors Mathematical Proof
This proof is only in two
dimensions.
In two dimensions, this only proves that the Incident and
Reflected rays are on parallel planes (yellow).
The rays could be drawn on planes (yellow) perpendicular
to (in & out of) the page.
Bicycle Reflectors Mathematical Proof
All light is reflected in
horizontal planes. No
light is lost to up and
down reflections
Looking from above, the
two mirrors act like a
single mirror as far as
the horizontal direction
of the reflected ray is
concerned.
Bicycle Reflectors Mathematical Proof
Slight changes in
the two mirrors
horizontal
orientation would
cause the reflected
light to miss the
Eye/Brain?
Bicycle Reflectors Mathematical Proof
Slight changes in
the two mirrors
horizontal
orientation would
cause the reflected
light to miss the
Eye/Brain?
Bicycle Reflectors Mathematical Proof
Slight changes in
the two mirrors
horizontal
orientation would
cause the reflected
light to miss the
Eye/Brain?
Bicycle Reflectors Mathematical Proof
But All light is
reflected in a
horizontal plane.
No light is lost to
vertical reflections
so all Eye/Brains
see bright
reflected light.
If three mirrors are arranged like the corner of a
cube,they are called “corner cube reflector”or a
“retro reflector”. They are all at right angles to
each other,
In corner cube reflectors,the Incident ray and final
Reflected ray are parallel lines. They are in exactly
opposite directions.
But the light must reflect form each of the three
mirrors
Measuring the Distance to the Moon
Laser ranging Corner
Cube Reflectors were
positioned on the Moon
in 1969 by the Apollo 11
astronauts.
Laser pulses beamed at the reflectors from Earth, help
scientists determine the distance between the earth and
Moon to an accuracy of about 3 centimeters.
Seeing Things
Making Corner Cube or Retro Reflectors
Precut Corner Cube Reflector mirrors are
available at STAO Store. The following shows how
to finish assembling them.
All mirrors will last a very long time if the back is
covered with duct tape. BUT Be careful you do not
damage the coating on the back by trying to
remove or adjust duct tape.
You can often obtain scrap glass mirrors from
Window & Mirror companies at reasonable prices.
Seeing Things
Making Corner Cube or Retro Reflectors
The Precut Corner Cube Reflector mirrors are
shipped flat in order to reduce shipping costs.
They look like the above picture
Seeing Things
Making Corner Cube or Retro Reflectors
Fold the top two corners together as shown in the
next series of slides
Seeing Things
Making Corner Cube or Retro Reflectors
Fold the top two corners together as shown in the
next series of slides
Seeing Things
Making Corner Cube or Retro Reflectors
Fold the top two corners together as shown in the
next series of slides
Seeing Things
Making Corner Cube or Retro Reflectors
Fold the top two corners together as shown in the
next series of slides
Seeing Things
Making Corner Cube or Retro Reflectors
Flip over and
Seeing Things
Making Corner Cube or Retro Reflectors
Flip over and duct tape the back
Seeing Things
Making Corner Cube or Retro Reflectors
Flip over and duct tape the back
Seeing Things
Making Corner Cube or Retro Reflectors
Flip over and duct tape the back
Seeing Things
Making Corner Cube or Retro Reflectors
Trim the access duct tape from the back
Seeing Things
Making Corner Cube or Retro Reflectors
If you have extra small square mirrors you can
also make your own corner cube reflector.
If possible use triangular mirrors.
Seeing Things
Making Corner Cube or Retro Reflectors
Dust tape the first two mirrors at 90°.
Seeing Things
Making Corner Cube or Retro Reflectors
Dust tape the first two mirrors at 90°.
Seeing Things
Making Corner Cube or Retro Reflectors
Dust tape the first two mirrors at 90°.
Seeing Things
Making Corner Cube or Retro Reflectors
Dust tape the first two mirrors at 90°.
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirror on top
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Place the next mirrors on top and duct tape
Seeing Things
Making Corner Cube or Retro Reflectors
Flip over
Seeing Things
Making Corner Cube or Retro Reflectors
This is the corner cube reflector
Seeing Things
Making Corner Cube or Retro Reflectors
This is the corner cube reflector that is nearly
identical to purchased ones
The area outside the dotted lines can cause
confusion as the light ray must reflect from all
mirrors if it is to reflect directly back at the
origin of the incident ray.
Bicycle reflectors use this shape to reflect light
back light ray must reflect from all mirrors if it
is to reflect directly back at the incident ray
Bicycle reflectors use this shape to reflect light
back light ray must reflect from all mirrors if it
is to reflect directly back at the incident ray
Bicycle Reflectors
and the Distance to the Moon
It is certainly true that principles cannot be more
securely founded than on experience and consciously
clear thinking.
— Albert Einstein
In other words, Check it out! Does the theory work?
Arrange three mirrors so they form the corner of a
cube. Then shine a laser pointer at them and see if it’s
reflected back regardless of the direction you shine
the laser. Misting with a spray bottle will make the
laser beam visible. Try a Bicycle Reflector