All rays coming from a given object point get mapped to a single point in the image providing the object is at “focus”.
- it captures much more light → good
- objects out of focus get blurred → bad
Lenses, like Pinhole cameras, perform perspective projection.
#Snell’s Law
Lenses are made of glass or plastic with refraction indexes much larger than air (~1).
#Thin Conex Lens
Here’s how a thin convex lens focuses multiple rays coming from a point in the object on a single point mapped in the image (resulting in a sharp bright image at the focused area).
The equation that determines the ideal distance is:
#Magnification in Lenses
Magnification is defined in the same manner as before:
$$ m = \frac{h_i}{h_o} = \frac{i}{o} $$
See [[Slide2-Image Formation.pdf#page=25|proof]] here.
#Magnification in Two Lenses
When applying magnification in two lenses, their magnification factors get multiplied.
$$ m = m_1 \cdot m_2 = \frac{i_1}{o_1} \cdot \frac{i_2}{o_2} $$
#Focus in Lenses
Aperture: diameter of the lense $D = f/N$ (could be defined by the F-number (N))
A point being in focus means that all rays hit the detector at a single point. Out of focus means they hit detector at multiple points. (one single point will be mapped to a blurry circle)
There’s a “plane of focus” and points not mapped one-to-one on it will be represented by a disk.
The formula for calculating the blur circle diameter is:
Small apertures tend to behave like a pinhole (less light, less blur). In order to focus a defocused image, we can:
- Move the object to the object plane
- Move the image plane
- Move the lens
- Change the aperture
Slide2-Image Formation, p.33
Image Formation