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:
- A ray, parallel to the axis (on-axis), refracts and goes through f1.
- A ray, that goes through f1, refracts and leaves the lens "on-axis".
- 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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