• Throughout, we will assume thin lenses, and we won't have precise definitions for some concepts.
• CS 178 (Spring 2014) has been an amazing course with detailed material.
• CS 179 Course Schedule

§ Focal Length Physically

• Recall that the focal length of a thin lens is the location at which lines at infinity entering the lens all merge.
• Physically, this amounts to the distance from the lens to the focal point.

§ Focal Length Photographically (1. Zoom)

• If we have a real physical object of height $1$, distance $1$ from the lens. and let the projected height be $h$ on the focal plane.
• Then, we see that $1/1 = h/f$, so $h = f$. In general, we will have that $h \propto f$, so the focal length is proportional to the zoom factor.
• So, 'Zoom lenses' (Which support multiple focal lengths) report the zoom factor in terms of focal length. For example, a 24-70mm lens has a zoom factor of 70/24 = 2.9x.

§ Focal Length Photographically (2. Field of View)

• Suppose we have a fixed screen height $w$. Now, we want to understand what angle of vision we can capture on the screen height $w$.
• We have $\tan(theta/2) = (w/2)/f$. Thus, $theta = 2 \arctan(w/(2f))$. So, $theta$ decreases as $f$ increases.
• So, if we want a wide angle lens, it must have a small focal length.
• Easy way to see this: keep a triangle with a fixed base (this is the sensor) at $y = 0$. Move the apex of the triangle (this is the lens) closer to the base. As we do this, the angle at the apex increases.
• The angle at the apex, when extended, corresponds to the 'extent of the object' that can be captured on the sensor.
• Two extreme cases: When the apex 'lies on' the base, the angle is 180 degrees, and the object can be as large as we want.
• Another extreme case: When the apex is very very far away, the angle is very small, and the object can be very small.

§ Aperture Physically

• The aperture is measured in units of $f/k$, where $f$ is the focal length.
• The units are called 'f-stops'.
• Why stops? Well, cause a dude called 'Waterhouse' designed an interchangeable 'stop' (a part of an optics device that can stop light) to control the amount of light that enters the camera.
• Now, while aperture itself (physically) is measured in diameters, what it lets in (light) has units of area. So, increasing the diameter by $\sqrt 2$ doubles the light.
• Thus, f-stops are available in f/1.4, f/2, f/2.8, where each has an aperture that is $\sqrt 2$ smaller than the previous one. Consequently, they let in half the light of the previous one.

§ Aperture Photographically (Depth of Field, Maximum Circle of Confusion)

• My intuition is the following. If we have a pinhole camera, then everything is sharp, since we get a 'single' point of light from each point in the scene. But this corresponds to aperture of $\epsilon$ (very small).
• As we increase the aperture, we get a cone of light from each point in the scene.
• This means that not everything lies on the focal plane.

§ Shutter Speed Physically

• Amount of time shutter remains open

§ Shutter Speed Photographically (Motion Blur)

• Longer the shutter remains open, more blurry stuff looks.

§ ISO Physically

• Gain on the physical sensor, before analog to digital conversion.

§ ISO Photographically (Grain/Noise/Light)

• Results in a bunch of noise when increased, but also lets in more light.

§ SLR (Single Lens Reflex)

• Light enters camera through aperture, and is focused on a strip of film.
• But to see what one is shooting, a mirror in front of the film bounces the light to the viewfinder that lets us preview. (This is the 'reflex' part).
• When we press the shutter button, the mirror moves away to allow the light onto the film, exposing it.
• DSLR is the same, except the film is digital.

§ Mirrorless

• Digitize the entire process above.
• The light hits the screen, and the data from the sensor is sent to the viewfinderm which is a digital screen.
• This means that the camera can be smaller, since we don't need a mirror, and also, the postprocessing can also be shown in the preview.

§ APS-C

• This is the image sensor format (format is physical, so size and shape).