of lenses and how these little pieces of glass make filmmaking possible.

People have been fascinated by the properties of translucent crystals and glass since antiquity

long before we understood any about light.

The first lens or oldest artifact that resembled a lens is the Nimrud lens - dating back 750

to 710 BC Assyria. The intended use of this piece of

polished crystal is still a bit of a mystery - perhaps it was just used a decorative stone, perhaps it was

used as a magnifying glass for making intricate engraving or

perhaps it was used as a fire starter.

The Ancient Greeks and Romans give us the first recorded mention of a lens in Aristophanes'

play “The Clouds” from 424 BC mentioning a burning-glass -

a fire starting magnifying glass made out of water filled glass sphere. In fact our

word “lens” comes from the Latin for Lentil which is shaped like a

double convex lens.

But these first lenses were either polished crystals or water filled glass vessels - the

idea of producing a lens purely out of glass didn't come

about until the middle ages.

It began with this man: Abu Ali Hasan Ibn Al-Haitham, also known as Alhazen. Born in

Basrah in 945AD in what is now present day Iraq, he settled in

Spain where his ideas would found the basics of the scientific revolution including theories

on vision, optics, physics, astronomy and mathematics. He

was the first to accurately describe the eye as a receiver of light rather an emitter of

rays that the Greek scholars Ptolemy and Euclid believed. He

was the first to describe the camera obscura - a pinhole camera that had been known to

the Chinese but never written down.

But for our story today, Alhazen was key for his theories on glass lenses. Based on his

works, European monks began to fashion reading stones,

hemispherical pieces of polished glass that could be placed on top manuscripts to make

them easier to read.

This, as you could imagine, was a godsend for monks with aging eyes…But why stop there? As glass making became

more sophisticated, Italian glassmakers began making reading

stones thinner and even light enough to wear. The first spectacles appeared in Venice between

1268 and 1300 AD. This mid-14th-century frescos by

Tommaso da Modena, featured monks donning the trendiest and most sophisticated wearable

technology of the time.

But Lenses weren't just for utility and fashion - they were about to be used for important

scientific study - that is being able to see things really

far away and really close up. The first refracting telescopes for astronomy were built by Dutch

spectacle makers in 1608 and refined by Galileo in

1609. A few years later Galileo would alter a few elements on the telescope and create

the world's first microscope.

From opening up the vast cosmos, with Galileo observing the moons of Jupiter to inner space

revealing to Robert Hooke the microscopic cells furthering

our understanding of biology - the lens has been both a literal and metaphorical fire

starter for humanity's scientific understanding.

This is a good time in our story to stop and look at the science of how lenses work. It's

always a little tricky when looking at the history of

science because a lot of the basic understandings we take for granted today were total mysteries

to scientists back then..

Having said that though, let's cheat and apply some 20th century understanding to the

discoveries being made by people like Willebrord Snellius,

Christiaan Huygens, and Isaac Newton.

Let's start with a 20th century understanding of light. We now know that Light is a form

of electromagnetic radiation which also includes radio,

microwaves, infrared, ultraviolet, X-rays and gamma waves.

All electromagnetic radiation travels at the speed of light in a vacuum - a constant 299,792,458

meters per second (approximately 186,282 miles per

second). That's regardless of who the observer is.

But that is the speed of light in a vacuum.

When light travels through a medium, the electrons inside the medium disrupt the path light ray

- slowing it down. The amount of slowing down is

described by the material's “index of refraction” - the larger the index of refraction

- the slower light travels through that medium.

Air has a miniscule index of refraction: 1.000293 - so for anything that's not on a planetary

scale, it's negligible. Water has an index of 1.33. If

we shine a laser through an aquarium at an angle, we can see how the slowing down of

light bends the light beam as it travels through the water, once

it reaches the end of of the aquarium, the light beam continues along it's original angle.

But if we curve the surfaces of the entrance and exit points we can bend the light and

direct light beams along a different path.

To demonstrate I've created a few homemade lenses using gel wax. Using a square piece

of gel wax and a protractor we can determine the index of

refraction using Snell's law.

Now if we curve the surface - into a convex shape - here a double convex lens - we can

redirect a light beam. Convex lens will bend light inwards

where as a concave lens - here a double concave lens, will diverge light.

There's only so much you can do with homemade lenses. To explore the properties of lenses

we stepped up our experiments with real glass lenses and a

visit to YouTube Space in Los Angeles.

The first and most important part of a single lens is the focal length. The focal length

is the distance from the lens to the point where collimated

light rays, that's parallel light rays, converge. You can think of collimated light

as light coming from a very far away point in space - like the

sun. Using a pair of laser pointers and some fog, we can see that this convex lens has

a focal length of 130mm.

For determining the focal length of a concave lens - we would continue our diverging lines

backwards - this double concave lens has a focal length of about 170mm

So now let's talk about how we get a real focused image using a single lens. When the

object we're trying to focus on is very far away - we're dealing

with collimated light rays. So in order to get a focused image, we would need to our

imaging sensor at the focal length.

But not all light rays are collimated - light radiates from objects in a spherical fashion

and closer you are to something the more divergent the

light rays. So how does a lens focus the light from an object that's close? To solve this

question we have the thin lens equation 1/Distance from the

Object + 1/Distance to the image plane = 1/focal length.

First off let's talk about a really far away object. As the Distance to the Object

approaches infinity, the 1/distance to object approaches zero -

leaving us a little algebra and the distance to the image plane equals the focal length.

So far so good - but let's try to focus on something closer. Don't worry, we won't

get too crazy with the math - in fact it's easier to visualize with

a lenses and a couple of laser pointers and do some lens ray tracing.

We'll fire our first laser perpendicular to the lens. Once it hits the lens, it will

bend toward the focal point on the far side of the lens Now we'll

fire our second laser - this time aiming toward the focal point in front of the lens, so that

when it hits the lens it will be bent and exit in lens

at perpendicular angle. Where the lasers first meet in front of the lens is at our object

distance and where the lasers converge behind the lens is

where the focused image will be.

So in this first example, our object distance is 260mm and our focused image will be also

at 260mm using this 130mm lens. Notice how both distances

are exactly 2 times the focal length - and the math checks out.

Let's try another example this time with the object distance at 340mm. Using the same

130mm lens the focused image will be at 210mm.

Notice how the beams converge beneath their origins, this means the image created will

be upside down. Laser ray tracing can be a bit abstract - let's

try it with a light bulb as our object and a piece of paper as our image sensor. Putting

the lightbulb at 340mm in front of the lens and paper at 210

does indeed yield a real focused image. Notice how shape of the light bulb filament is upside

down in the projected image and if we move our imaging

plane closer or further away we'll see the image go in and out of focus.

Now this works for a single thin lens with an object distance of over say about 2 times

the focal length. As the object distance gets closer to 1

times the focal length - the imaging distance approaches infinity - sort of the reverse

of what happened when we talked about collimated light. But

what happens when the object is inside the focal length?

Well the answer is we'll have a negative image distance. It's hard to simulate with

my experiment design but what you'll notice is the light never

comes to a focus past the lens - instead it looks like it's even more divergent. Let's

use a diagram to make it easier to see - again one ray

perpendicular to lens which bends to the focal point on the far side of the lens - and the

second ray coming from the focal point through the lens to

create a perpendicular ray.

The key here is our eyes and brain don't know that light is being bent by the lens

- we assume that all light rays are straight and continuous. So if

we follow the light rays back from the lens we end up constructing a virtual image behind

the object - right side up and magnified- this is how a

magnifying glass works.

The real fun occurs when we bring more than one lens into the mix. Telescopes use an objective

lens with a long focal length and an eyepiece lens for

focusing - the lenses have to be placed inside their focal lengths in order to work. A microscope

switches out the objective lens with its long focal

length for a lens with a very short focal length.

Combining multiple lenses also allows us to change the magnification - here is a model

of an afocal zoom lens - using two convex lenses with a concave

lens in between. As we move the concave lens we change the distance of the beams entering

the lens system. Focus on the bright green beams, the others

are reflections created by inferior glass. Notice how the beams change distance as I

move the middle double concave lens. Using a light bulb in place

of the lasers and an aperture on the final focusing lens to increase the sharpness, we

can see this zoom lens in action.

The demand for better and better lens systems for scientific discovery kept lensmakers busy

throughout the 17th and 18th century, but the coming age

of photography would bring a whole new game to town.

THE INFANCY OF PHOTOGRAPHY

The very first lenses used for photography in the 19th century were single element pieces

of glass just like in our science demonstration. But the

problem is, there's a lot of photographic issues from using just one lens including

Chromatic Aberration - that's where light of different

wavelengths get bent differently as they pass through a lens. Anyone who wears glasses can

see this effect when they look at a neon sign that has blue

and red lights, Spherical Aberration - where not all light rays are converging at the focal

point, and Coma Aberration - where off axis light smears

creating a comet like tail. These are just a few of the problems image makers have to deal with.

The first widespread photography process - the French originated Daguerreotype used a lens

by French lensmaker Charles Chevalier in 1839. This lens

was an achromatic doublet, cementing a biconvex element of crown glass with a biconcave element

of flint glass. These two types of glass have

different properties and combined these lens greatly reduced chromatic aberration leading

to sharper images. This early lens used an aperture, a small

hole that reduces the angle of the light rays coming in which further increases sharpness

but reduces the amount of light available for the film. With

an aperture of f16 - f stop is the ratio of the the lens' focal length to the diameter

of the aperture, this lens was very slow - taking twenty to

thirty minutes for an outdoor daguerreotype exposure. Because of this limitation, this

lens became known as the French Landscape Lens.

For portraits, especially indoor portraits, a new type of lens configuration was needed.

In 1840 the French Society for the Encouragement of National

Industry offered an international prize for just such a thing. Joseph Petzval a Slovakia

mathematics professor with no background in optics with the

help of several human computers from the Austro-Hungarian army took up the challenge and submitted his

design in 1840 - the Petzval Portrait lens.

This was a four element lens which had an aperture of f3.6 - much faster than the Landscape

lens - a shaded outdoor sitting would only take a minute

or two and with the new wet collodion process for photography and this lens could even expose

an indoor portrait in about a minute.

But Petzval didn't win the prize… mainly because he wasn't French, but his lens would

go on to be a dominant design for nearly a century - it was

sharp in the middle but fell out of focus quickly on the sides which gave those portraits

from the 1800s that soft edge halo focusing effect.

And although Petzval lens was a mathematically devised lens, lensmaking would resort to trial

and error for the next 50 years which included the first

wide angle Harrison & Schnitzer Globe lens of 1862 and the Dallmeyer Rapid-Rectilinear

(UK) and Steinheil Aplanat from 1866.

These four lenses, The French Landscape, the Petzval Portrait, the Globe and the Rapid-Rectilinear/Aplanat