Optics Part One (What can we do with light?)

A.Types of lenses.

 1. convex-convex lenses
 2. concave-concave
 3. plano-concave
 4. plano-convex
 5. concave-convex

If a lens is thicker in the middle, rays will converge;

if it's thinner in the middle, rays will diverge.

B.Ray Tracing

f1 = Focal Point - point at which parallel rays converge after passing through a convex lens

f2 = a point that is 2 times the focal length from the lens

C (center of curvature) = a point that is the center of a spherical mirror, and generally 2 times the focal length from that mirror

Rules:

1. A ray, parallel to the axis (on-axis), refracts and goes through f1.
2. A ray, that goes through f1, refracts and leaves the lens "on-axis".
3. A ray that passes through the center of the lens does not refract.

C. Calculating f

${f}$ - Focal Length - distance from the center of the lens/mirror to the focal point.

${d_{i}}$ - distance from the lens/mirror to the image.

${d_{o}}$ - distance from the lens/mirror to the object.

${\frac {1}{f}}={\frac {1}{d_{i}}}+{\frac {1}{d_{o}}}$ or ${\frac {1}{f}}={\frac {1}{p}}+{\frac {1}{d}}$

because p and d are interchangeable mathematically.

• real image- can be focused onto a surface
• virtual image- can see using the naked eye, but cannot focus onto a surface

Altmantl 23:52, 4 September 2007 (UTC)

D. Image Truths:

Object is...	Image is...	Size	Type	Orientation
At infinity	At f1	Point	Real?	Inverted?
Beyond f2	Between f1 and f2	Small	Real	Inverted
At f2	At f2	Same as Object	Real	Inverted
Between f1 and f2	Beyond f2	Large	Real	Inverted
At f1	Nowhere
Between lens and f1	Beyond Object?	Large	Virtual	Upright

E. f-number – a measure of the amount of light gathered by a lens or mirror.

A high number gathers less light, so (with telescopes) 5.6 may be better than 8. It is said to be "faster". By capturing more light, it can produce brighter images or images that take less exposure time. The lower number also has a wider field of view. In cameras, you may see f/ratio settings like: f/1.2, 2, 2.8, 4, 5.6, 8, 11, 16, 22. In telescopes, you may find: f/4, 5.4, 6, 8, 11. In cameras, "stopping down" to higher f-numbers produces a greater "depth of field" but forces a longer exposure time.

$f/ratio={\frac {f.l.}{diameter}}$

F. Magnification – number of times a telescope/microscope increases the size of an image

$M={\frac {f_{1}}{f_{2}}}$

where $f_{1}$ is the Focal Length of the Primary Mirror of a reflecting telescope (or the Objective Lens of a refracting telescope or Microscope) and $f_{2}$ is the Focal Length of the Eyepiece.

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External Links

• Northern Stars Planetarium
• University of Pennsylvania Physics Department
• McDonald Observatory at UT
• Hyperphysics
• Wish I had seen their animation before I made my own.
• Koreans do it too