How do lenses really work?

[LHACK4142]

I've been investigating photography a little but am confused on how lenses, and focal lengths, really work.  This question has been with me since I was a little kid playing with magnifying glasses, actually.  So, many pictures show light entering a lens as straight lines:

But if only light rays parallel to the lens could enter, you would only be able to see an area equal to that of the lens, right?  Since you can see the entire sun, and not just a lens-sized portion of it (pictured), through a magnifying glass, this type of diagram must be incorrect.

Other images (below) show straight lines through the lens, which kinda confuses me; don't lenses specifically bend light?  And what are the lenses in these pictures supposed to be doing?

So, what exactly is a lens doing, and where are the light rays coming from, how are they being manipulated, and how are they ended up?

Edited March 10 by LHACK4142

[Ryaja]

So, light speed is not constant and light has a defined size. When a photon hits the glass at anangle one side slows down and therefore tilits it. Think hitting the water with one side of your ssto wing in KSP(this is the Kerbal forums ok!) so what is done with the lense is the parabolic/circular curve to make it all face the center point. And this essentially compresses the image coming in at the front to a point. You then go behind that and get a flipped but protected image. The further you move the lens away the smaller a portion of the total for your getting in zoom. The closer you get the more of said range you see. So a lens with a long focal length has less fov equalling zoomed in images while the opposite is also true, a lens with a short focal length has a wide fov, a zoomed out image. I hope that wasn't incoherent ramblings from my mind and others actually understand it!

Just now, Ryaja said:

So, light speed is not constant and light has a defined size. When a photon hits the glass at anangle one side slows down and therefore tilits it. Think hitting the water with one side of your ssto wing in KSP(this is the Kerbal forums ok!) so what is done with the lense is the parabolic/circular curve to make it all face the center point. And this essentially compresses the image coming in at the front to a point. You then go behind that and get a flipped but protected image. The further you move the lens away the smaller a portion of the total for your getting in zoom. The closer you get the more of said range you see. So a lens with a long focal length has less fov equalling zoomed in images while the opposite is also true, a lens with a short focal length has a wide fov, a zoomed out image. I hope that wasn't incoherent ramblings from my mind and others actually understand it!

This is mostly my guesses from the shower knowing the basics.

[Nuke]

its all about wavefront propagation.

check out huygens optics channel on youtube. lot of really cool info about lenses, telescopes and everything. he even makes monolithic cassegrain scopes out of a single piece of glass.

Edited March 13 by Nuke

[Vanamonde]

Thread moved to the Science sub since there's actual sciencing being discussed. 

[AckSed]

A read of xkcd's What if? on Fire By Moonlight gives a reasonable explanation of how optics and light-gathering by a lens works in explaining why you can't set fire to anything with moonlight, no matter how large a lens: for one, you can't exceed the surface temperature of a heat/light-emitting black body, and the Moon's is ~100 deg. C; for another:

Quote

Except lenses don't concentrate light down onto a point—not unless the light source is also a point. They concentrate light down onto an area—a tiny image of the Sun [or Moon].

So the diagrams are simplifying for illustration because you can't show every beam of light entering, but also lying in the process. Lenses do gather light from as many directions as possible to project an image. The "point of sharp focus" is where the smallest image gathered by the main lens is. Focal length is how far behind the point of sharp focus the lens (or group of lenses) projects the now-inverted image. More on focal length, field of view.

The double lenses are for reducing chromatic aberration (the rainbow at the edge of images), as different wavelengths of light are refracted differently to a greater or lesser degree by the same material, so (at least in the earliest achromatic doublet lenses) two different types of glass that form a single lens were used, the second type with a different refractive index to bend the light back.

 

[Terwin]

Straight lines are used because they are easier to draw and visualize.

Actually the lense will bend all light that hits it.  This is part of why you generally have camera lenses in an opaque black tube: to minimize extraneous light that could interfere or obscure part or all of the image .

Much like friction-less inclines, those lines are a simplification to provide a clearer explanation, not a fully accurate reflection of reality.

[Hannu2]

Those lines and ideal lenses are oversimplifications (called geometrical optics). They can be used to understand very basic operation of single lense but real life is much more complicated and generally you have to solve Maxwell's equations with suitable boundary conditions, which are defined by lenses' geometry and material properties. Most lenses are for dispersion correction. Refractive indices of all real materials are dependent on wavelength which leads to chromatic aberration.   It is managed to acceptable levels by using suitable set of different lenses made from different materials which dispersions cancel each other. Then there are lenses for correcting geometric errors (often aspherical shapes). And all corrections should happen at all focal distances (and lengths in zoom lenses). There are usually 10-20 lenses in several groups in modern camera lens which acts as single "ideal lens".