Geometrical Optics in a Nutshell
- Images are classified as being real or virtual.
- Real images are formed when light rays converge. Real images can be projected onto a screen and are always inverted in appearance.
- Virtual images are formed as the brain imagines that reflected or refracted light rays converge back from their diverging paths. Virtual images cannot be projected onto a screen and are always upright.
- Plane mirrors, convex mirrors, and concave lenses always produce virtual images. The virtual images produced by convex mirrors and concave lenses are always smaller than the object.
- Concave mirrors and convex lenses produce both real and virtual images. The real images may be larger or smaller than the object, whereas the virtual images are always larger.
- For a curved mirror, the focal length is equal to half the radius of curvature.
- If an object is placed at the focal point of a concave mirror or a convex lens, no image will be formed.
Principle Rays for Mirrors
- Draw ray from top of object parallel to the optical axis and is reflected back through a focal point.
- Draw ray from top of object through center of curvature. Ray reflects back on itself.
- Draw ray from top of object through focal point and on to mirror. After reflection it runs parallel to the optical axis.
Principle Rays for Lenses
- Draw ray from top of object parallel to the optical axis, through the lens and then passing through a focal point.
- Draw a ray through the center of lens. Path remains undeviated.
- Draw a ray through focal point and on to lens. After lens it runs parallel to the optical axis.
Refraction in a Nutshell
- Snell's law governs the refraction of light through transparent media.
- The ratio of the speed of light in air to the speed of light in a transparent medium is called the absolute index of refraction.
- The speed of light in a transparent medium can be obtained using Snell's law and is inversely proportional to the absolute index of refraction for the medium.
- When the angle of incidence exceeds the critical angle, total internal reflection occurs and no light is refracted.
- Fiber optics communication, in which information is processed along hair-thin glass fibers, works because of total internal reflection.
- sin i/sin r=v1/v2=n2/n1
- sin i/sin r=c/v2=n2
- sin ꝋcritical=n2/n1 (n2<n1)