Exploring the basics of the Rochester Cloak

with an Invisibility Kit by

Making Invisibility VISIBLE

– for Muggles

Harry’s Cloak• Light weight and portable

• Full coverage of a human sized object from any angle

• Allows you to see the background clearly

• Relies on the unique optical properties found in the fur of DemiGods

• Not for Muggles • YET?

Romulan Space Ships• Free floating

• Full coverage of a space ship sized object from any angle

• Allows you to see “right through it” into outer space without distortion

• Relies on the unique optical properties found in something the Romulans will kill you over before they give it to you

• Not for Earthlings • YET?

Invisibility in the classroom• Engaging, enticing, exciting!!

• Easy to demonstrate: portable, affordable, do-able at the high school (middle school?) level

• Draws on or puts to use topics, formulas, ideas, skills and practices we know we need to teach

Invisibility is a function of light• Visible

• Enough visible light (400-700nm) from a source bounces off an object and into our eyes to be detected.

• Invisible • Not enough light (too small… too far away) • Light not in the visible spectrum (IR, UV)• Does not bounce off the object and into our eyes

• Blocked (absorbed) • Bent (refracted)

Light is an Electromagnetic Wave

What can control both the electric and magnetic fields?

The Electromagnetic Spectrum

What can control light in the visible range?

Refraction• Light changes speed as it travels from one media to

another (air to glass for example)

• Light always bends towards the denser medium (normal)

# 1: Index of Refraction

• 1 – fill with water, no difference in index of refraction• 2 – pyrex and oil have the same index of refraction• Benefits: inexpensive, easy, portable, demonstratable• Limitations: liquid, colorless

# 2: Metamaterials- Nano Structures

• Nano sized human made molecular arrangements that suppress scattered light waves

• Break the laws of Physics!! Reverse Snell’s Law

Limitations of Meta Materials• Very, very expensive to

produce or demonstrate• Very, very small • Neither portable nor

invisible• Many do not work in the

visible range – Stealth, Radar

• You cant see out!

Rochester Cloak• First 3D visible light

invisibility cloak• Developed at the

University of Rochester in NY

• Creates “regions of invisibility” that can completely hide objects.

• Uses refraction through a conventional 4 lens system.

Rochester Cloak• Hides real objects

from several angels• Allows the background

to be seen clearly• Portable and EASY to

demonstrate• Inexpensive• Paraxial Ray Optics

Cloaking – Linear Algebra

• but… Let’s start at the beginning..

What it does• As light reflects off of the background, it refracts as it

passes through the lenses creating “cloaked regions”.• When an object is placed inside of a cloaked region, light

from the background passes around object causing the background to be visible, rather than the object!

Refraction with Lenses: Convex• Lenses redirect light• Convex lenses are thicker in the middle and thinner at

the edges• This shape causes rays to bend towards the center of

the lens.

Refraction with Lenses: Concave• Lenses redirect light• Concave lenses are thinner in the middle and thicker at

the edges• This shape causes rays to bend towards the center of

the lens.

Focal Length/Point- Predictable!!!• All rays meet at a point called the

FOCAL POINT• The distance from the lens to the

focal point is called the FOCAL LENGTH

• The Focal Length is predictable• Critical info for understanding

Image formation

Rochester Cloak: • Cloak depends on the spacing between the lenses

• Distance between first two lenses• Parallel rays are refracted to focal point by lens 1• Resultant rays source at exactly f2 from lens 2• So… rays emerge parallel from lens 2

Optics Matricies: Linear Algebra

Smith Matricies

Rochester Cloak Setup

• Two pairs of convex lenses• Pairs having focal lengths f1 and f2

• F1 focal length is (150mm)• F2 focal length is (50mm)• Set up in straight line

• f2 lenses in middle, f1 on outside• distance between f1 and f2 lenses

on ends• d1=d3=f1+f2

• distance between f2 lenses in middle

• d2=2f2(f1+f2)(f1-f2)

Build your own cloak: Set up1. Place lenses in lens holders. Keep track of focal lengths.

TIP: thicker lens has shorter focal length.2. Stick graph paper to wall at end of long surface.3. Place one f1 lens at zero mark.4. Place one f2 lens 200mm from first lens. TIP: measure

from surface of the lenses, not centers!5. Place other f2 lens 200mm from second lens. Again,

measure from the surface!6. Lastly, place remaining f1 lens 200mm from third lens.

Build your own cloak: testing1. Use a LASER pointer to check that lenses are

aligned:1. Shine LASER through centre of first lens towards graph

paper.2. Beam should emerge through all four lenses unchanged:

no bigger or blurrier.• Stand sevral inches from first lens.

• Crouch to be on eye-level with lenses.• You should see the graph paper unmagnified through the

lenses.• Have someone move a pen or other long, thin object

between lenses 2 and 3. Object should disappear towards top and bottom of lenses.

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