Chapter 4: Geometric Optics How is light collected and focused to form images?. Geometric Optics. Reflection: Light bouncing back from a surface. Refraction: Light traveling from one transparent medium to another. Two parallel descriptions: Wave optics – “Wavefronts”
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How is light collected and focused to form images?
Light bouncing back from
Light traveling from one
transparent medium to another.
Location: 40 cm to left of mirror
Size: Same as the object (M=1)
Location: At the focal point
Location: q = -20 cm (behind the mirror)
Size: M=2, so 10 cm size
F1 (Marginal Rays focus here)
F2 (Paraxial rays focus here)
Image without spherical aberration
The index of refraction of a certain type of plastic is 1.7. Find the speed of light in this plastic.
1.765 x 108 m/s
When light passes into a new medium, its frequency remains constant and its wavelength changes.
One side of wave front slows down, and the entire train of fronts twists. Analogy: right front tire of vehicle enters mud, twisting vehicle to the right.
A ray of light traveling in air strikes a glass surface (n = 1.5) at an angle of 240 from the normal. At what angle will it be refracted in glass?
Given: Sin(240) = 0.407, Sin(15.70) = 0.2713
Sun appears flatter at sunset
Things appear shallower in water
Dispersion and rainbows
Or Converging Lens
Or Diverging Lens
+ Focal Length
(Like Concave Mirror)
- Focal Length
(Like Convex Mirror)
q = -100 cm (To the left of the lens, virtual)
M = 5 (Magnified)
q = 60 cm (To the right of the lens, real)
M = 5 (Magnified)
Image without chromatic aberration
Image / Light Carriers:
Bundles of fibers
Image Intensifiers / Magnifiers /
Inverters: Tapered fibers.
Fiber Optic Sensors: Special fibers used for sensing
pressure or temperature changes.
Losses are minimum at 1.5 mm wavelength!
After several km
through a fiber
have higher refractive
index so they travel
slower through the fiber.
Solution: Use lasers with
high spectral purity.
Local area networks
Long distance applications
Near Point = 25 cm
Far Point =
~ 1.5 mm under bright light
~ 6.0 mm under dim light
Image size = Hi
Object size = Ho
Effective center of cornea + lens
Resolving power (Limit of visual acuity):
Two points must be separated by at least 1/60th of 1 degree.
This means a separation of 0.1 cm at near point!
What is the smallest separation between two points on
the retina so the two points are seen as separate points?
(Hint: Take Ho = 0.1 mm, and do = 25 cm)
Note: The size of a single cone is about 5 mm!
For scotopic vision this acuity is much less.
Hi = 6.8 x 10-6 m
Short FL Lens
Small Image Size
Large Field of View
Long FL Lens
Large Image Size
Small Field of View
That's Seattle about 2 miles away. focal length 36 mm
focal length 138 mm
focal length 276 mm
focal length 432 mm
A photographer uses a camera with 50 mm focal length lens to photograph a distant object. He then uses a 150 mm lens to photograph the same object. How will the height of the object compare on the two resulting photographs? How do the areas compare?
Image size increases by a factor of 3
Area decreases by a factor of 9
Note: Brightness changes by a factor of 2 between adjacent f#’s.
Lenses with the same f# produce the same intensity on the film plane.
D = 12.5 mm
f# = 16
Brightness decreases by a factor of 16
Suppose a proper exposure of a film could be achieved by taking a picture at 1/50 s with f# = 8. If under the same light conditions, we wished to change the exposure time to 1/200 s, what f# should we choose?
f# = 4
F# = 2
F# = 8
F# = 22