The Digital Camera: Where are we going and why?

I am writing The Digital Camera posts for this blog to explain the physical and technical principles that enable much of the magic in modern digital cameras. Although the field of optics is highly mathematical, I believe many of the important principles can be understood by using just a few basic notions from algebra and trigonometry. The technical aspects of photography can be tricky, but my objective for these posts is to help you understand some key concepts so you can provide your own answers to questions like these:

  • What does it mean when the display on my point-and-shoot camera says f/5.6?
    The f-number 5.6 means that the focal length of the lens is 5.6 times larger than the width of the lens aperture.
  • I took a picture with my point and shoot camera and it has the same field-of-view and f-number as a picture my friend took with their full-frame SLR. My camera has 14 megapixels; their SLR has 10 megapixels. Because I have more pixels, will an enlarged print of my picture look as good or better than theirs?
    No, it will likely look worse. The detector on the SLR is probably over 5 times wider than the detector on the point-and-shoot, and, because of that, the effects of diffraction will cause the point-and-shoot picture to be over 5 times as blurry. The diffraction blur for the point-and-shoot picture might be about twice as big as a pixel; whereas the diffraction blur on the SLR would be about twice as small as a pixel.
  • Why does a 300mm f/2.8 lens cost nearly four times as much as a 300mm f/4 lens?
    The maximum aperture-diameter for the 300mm f/2.8 lens is about 107mm, and the total aperture area is about 9,000 square millimeters, or 14 square inches. For the 300mm f/4 lens, the maximum aperture-diameter is about 75mm and the aperture area is about 4,420 square millimeters, or about 7 square inches. It costs much more to correct aberrations for 14 square inches of glass than it does for 7 square inches.
  • Why can’t I get as close to a flower with my 100mm macro lens as I can with my 50mm macro lens?
    Mostly because of something called the lens equation.

These answers refer to things called the focal length, aperture, f-number, diffraction, aberrations, and the lens equation; the best way to master these concepts is by first understanding the physical principles on which they are based. Our introductory discussion on rays and refraction have and will address the way lenses bend light to form images, and, in the process, we’ll be prepared to master the concepts of focal length, aperture, f-number, the thin lens equation, and aberrations. We won’t cover diffraction until we talk about color and the wave nature of light.

Here is a recap of the things we’ve covered in our first few posts, and the things we’ll cover in upcoming posts:

Light Rays
We introduced the idea of light as rays that travel about 300 million meters per second in air, but slow to about 225 million meters per second in water and about 200 million meters per second in glass. We defined the ratio of the speed of light in air to the speed of light in a particular surrounding as the refractive index for the surrounding (1.33 for water, 1.5 for glass).

We used the discussion on shadows as a way to introduce the graphical representation of light rays. As a bonus, we learned why larger light sources (like umbrellas and soft boxes) make softer shadows.

We used the topic of reflection to think about the angles at which light rays travel and strike surfaces like mirrors. We also introduced the important phenomena of virtual and real images. As we did with shadows, we used the topic of reflection to strengthen our familiarity with the graphical representation of light rays.

The Principle of Least Time
This post used more mathematics than the previous posts, but the insight we gain by understanding this principle is well worth our effort. By thinking about where a lifeguard should enter the water to save a drowning person in the least amount of time, you’ll understand the essence of this principle.

In our post on refraction we’ll discuss the way light bends when it travels from air into water or glass. The mathematical equation that we’ll use to predict refraction contains a trigonometric function called the sine. This concept is critical, so, if you get confused by the mathematics, focus on the qualitative aspects of how light bends at boundaries. Refraction is the principle that optical engineers use to design camera lenses.

Total Internal Reflection
When light travels from a particular surrounding into one with a smaller refractive index (like from water into air), it is possible that the ray will reflect completely back into its surrounding. This is the reason it is easier for a fish to see you if you stand tall than if you hunker down.

The Pinhole Camera
We will wrap up our discussion on light rays by introducing the concept of a pinhole camera. We’ll use this post to further strengthen our familiarity with the graphical representation of light rays, and to motivate the need for — and emphasize the value of — a camera’s lens.

At this point we’ll be ready for a series of posts that use rays and ray diagrams to understand how lenses work.

© 2011 Timothy Schulz

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