1. A farsighted person’s cornea and lens focus images behind the retina
A farsighted person’s cornea and lens focus images behind the retina. Farsightedness is corrected with a converging lens.

2. A nearsighted person’s cornea and lens focus images in front of the retina. Nearsightedness is corrected with a diverging lens.

4. Telescopes and microscopes each use two converging lenses
Telescopes and microscopes each use two converging lenses. The objective produces a real image (case 1 for a telescope, case 4 for a microscope).

5. The image from the objective is formed inside the focal length of the eyepiece. The eyepiece magnifies this image (case 6).

6. Standard Microscope Image

7. When light enters a substance of lower optical density, it is bent away from the normal. “r” is greater than “i”. If “i” is gradually increased, “r” will reach 90° before “i” does.

8. The limiting angle of incidence that results in an angle of refraction of 90° is called the critical angle, ic. ic for water is 48.5° ic for crown glass is 42° ic for diamond is 24°

9. The index of refraction for a water/air boundary is:
The index of refraction for a water/air boundary is: n = sin r (air) / sin i (water)

10. When i is ic , r is 90°, and sin 90° is 1
When i is ic , r is 90°, and sin 90° is 1. So the previous equation can be converted to: sin ic = 1 / n n is the index of refraction relative to air. ic is the critical angle of this medium.

11. When the angle of incidence exceeds the critical angle, total reflection occurs.

13. Because of refraction, the sun’s rays are bent toward the surface of the earth. The sun can still be seen after it has passed below the horizon.

14. Because of this, a day is about 4 minutes longer than it would be.

15. Atmospheric refraction can produce mirages if the ground is so hot that the air close to the ground is warmer than the air at higher elevations.

16. A visible object appears to be reflected in water because that matches our previous experience.

17. This atmospheric refraction can make drivers see what appear to be wet spots on the road. These are actually refracted images of the blue sky.

18. Different frequencies of light travel at different speeds in transparent materials. Violet light travels about 1% slower in glass than red light.

19. Under certain conditions, this splits light into its spectrum; this is called dispersion.

20. Prisms produce dispersion
Prisms produce dispersion. Raindrops produce dispersion in the form of rainbows.

23. Lenses with a large aperture focus parallel rays near the edge of the lens at points nearer to the lens than the principle focus. This is called spherical aberration and results in fuzzy images.

24. Chromatic aberration results from the fact that different colors are refracted more than others. Violet light is refracted more than red light.

25. The focal lengths are different for different colors, so different colors focus at different points. Combining converging and diverging lenses can greatly reduce chromatic aberration.