Transforming My Office Into a Camera Obscura: A Study in Optics and Wonder
An exploration of camera obscura physics, aperture theory, f-stops vs t-stops, and diffraction, with my office as the experimental chamber
2016-12-09
Loading content...
An exploration of camera obscura physics, aperture theory, f-stops vs t-stops, and diffraction, with my office as the experimental chamber
There's something profoundly magical about the camera obscura: this ancient optical phenomenon that forms the theoretical foundation of all photography. The idea that light passing through a small aperture can project an inverted image of the outside world onto a surface has fascinated humans for over two millennia. So naturally, I decided to turn my entire office into one.
Camera obscura (Latin for "dark chamber") is an optical phenomenon where light passing through a small hole into a darkened space projects an inverted image of the outside scene onto the opposite surface. It's the fundamental principle behind every camera ever made: from ancient pinhole cameras to modern DSLRs.
The setup is deceptively simple: make your room completely dark, create a small aperture in one wall (usually a window covering), and the outside world will magically appear, upside down, on the opposite wall.
Understanding why camera obscura works requires diving into geometric optics and the behavior of light rays.
Light travels in straight lines (in homogeneous media). When light from an object passes through a small aperture, each point on the object sends light rays through the hole. These rays continue in straight lines until they hit a surface, creating a point of light.
The mathematical relationship governing the projection is based on similar triangles:
h'/h = d'/d
Where:
h = height of objecth' = height of projected imaged = distance from object to apertured' = distance from aperture to projection surface
The inversion occurs because light rays cross at the aperture. Light from the top of an object passes through the hole and strikes the bottom of the projection surface, while light from the bottom strikes the top. This creates a vertically and horizontally flipped image.
The size of the aperture is critical for image quality. Too large, and the image becomes blurry due to overlapping light cones. Too small, and diffraction becomes the limiting factor.
For a pinhole camera, the optimal aperture diameter can be calculated using:
d_optimal = √(2λD)
Where:
d = aperture diameterλ = wavelength of light (approximately 550nm for green light)D = distance from aperture to projection surfaceFor my office setup with a projection distance of approximately 4 meters:
d_optimal = √(2 × 550 × 10⁻⁹ × 4) = √(4.4 × 10⁻⁶) ≈ 2.1mm
This experiment provides a perfect opportunity to discuss the difference between f-stops and t-stops: a distinction that's crucial for understanding optical systems.
F-stop is a geometric measurement representing the ratio of focal length to aperture diameter:
f-stop = f/D
For a pinhole camera, the "focal length" is the distance from aperture to projection surface. So with my 4-meter setup and 2mm aperture:
f-stop = 4000mm/2mm = f/2000
This seems absurdly high compared to camera lenses (which typically range from f/1.4 to f/22), but it illustrates why pinhole cameras require such long exposures.
T-stops account for actual light transmission through an optical system. While f-stops are purely geometric, t-stops measure how much light actually reaches the sensor/film after accounting for:
For a simple pinhole (no glass elements), the f-stop and t-stop are essentially identical, making the camera obscura a "perfect" optical system in this regard.
As aperture size decreases, we eventually hit the diffraction limit: the point where the wave nature of light becomes more significant than its particle behavior.
The angular resolution limit due to diffraction is given by:
θ = 1.22λ/D
Where θ is the angular resolution in radians. For visible light (λ ≈ 550nm) and our 2mm aperture:
θ = 1.22 × 550 × 10⁻⁹ / 0.002 = 3.4 × 10⁻⁴ radians
At our 4-meter projection distance, this translates to a resolution limit of about 1.3mm: meaning fine details smaller than this will be blurred by diffraction regardless of the geometric optics.
One remarkable characteristic of pinhole optics is infinite depth of field. Unlike lens-based systems where only objects at the focus distance are sharp, a camera obscura renders everything from a few meters to infinity with equal sharpness (limited only by diffraction).
This occurs because the aperture is so small that the circle of confusion for objects at different distances remains negligible compared to the diffraction-limited resolution.
The extreme f-stop of a camera obscura (f/2000 in my setup) means the projected image is quite dim. The exposure time scales with the square of the f-stop, so compared to a camera lens at f/2:
Exposure Ratio = (f₂/f₁)² = (2000/2)² = 1,000,000
This means the camera obscura requires one million times longer exposure than a lens at f/2! This is why early pinhole photographs required exposure times measured in hours.
One surprising aspect of the camera obscura projection was the excellent color reproduction. Without any glass elements to introduce chromatic aberration or color casts, the colors appeared remarkably true to life, perhaps even more accurate than what we see through modern camera lenses with their complex optical corrections.
The contrast was also excellent, with deep shadows and bright highlights faithfully reproduced. This demonstrates the superiority of simple optical systems for color accuracy, even if they sacrifice light-gathering ability.
Creating a room-sized camera obscura required careful attention to light leaks:
I tested multiple aperture sizes by carefully punching holes in heavy-duty aluminum foil using needles of different diameters. The precision required is surprising: a difference of 0.5mm in aperture diameter significantly affects image quality.
One of the most fascinating aspects was watching the projected image change in real-time. Cars moving past, people walking by, clouds drifting across the sky: all appeared live on my office wall, inverted and magical.
This real-time aspect highlights something we often forget about photography: cameras don't just capture moments; they're continuously projecting the world onto the sensor. The shutter simply controls when we record that projection.
The camera obscura principle has been known since ancient times:
My office experiment connected me to this long lineage of optical investigation, from ancient philosophers to Renaissance artists to modern photographers.
There's something deeply satisfying about how perfectly the mathematics predicts the real-world results. The calculated optimal aperture size produced exactly the image quality the equations suggested. The geometric relationships held true. The physics worked as advertised.
This reinforces photography's foundation in science and mathematics: every image we capture is the result of photons behaving according to physical laws that have remained constant since the universe began.
This experiment reinforced several key optical principles:
Understanding camera obscura principles remains relevant for modern photography:
Despite understanding all the physics and mathematics, watching my office wall display a live, inverted view of the outside world never stopped being magical. This is perhaps the most important lesson: technical knowledge enhances wonder.
Every photograph we take is a technological miracle: photons traveling at the speed of light, carrying information about distant objects, focused by precisely curved glass elements, and captured by sensors that convert light into digital data. The camera obscura strips this down to its most fundamental level, revealing the magic that underlies all of photography.
You can view the complete documentation of this camera obscura experiment on my Flickr album. The images show various stages of setup, different aperture sizes, and the evolution of the projected image throughout the day.
The camera obscura experiment reminded me why I fell in love with photography in the first place: the intersection of art and science, the way technical understanding deepens appreciation for beauty, and the simple wonder of light itself.