| Unit 14. Geometrical Optics. |
|
Major Concepts |
| Unit 14. Geometrical Optics. |
|
Major Concepts |
| Wave Fronts | The surfaces of constant phase. |
| Rays | The radial lines pointing outward from the source and perpendicular to the wave fronts. |
| Plane Waves | Waves whose wave fronts are flat surfaces, i.e. planes. |
| Law of Reflection | The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection equals the angle of incidence. |
| Virtual Image | When the rays of light do not actually emanate from the image. |
| Real Image | When the rays of light actually do emanate from the image. |
|
Focal Length of a concave mirror |
F = R / 2 |
|
Focal Length of a convex mirror |
F = - R / 2 |
|
The Principle of Reversibility |
If the direction of a light ray is reversed, the light retraces it's original path. |
| Image Formation By a Convex Mirror |
Ray 1:
This ray is initially parallel to the principal axis
and therefore appears to originate from the focal point
F of the mirror.
Ray 2: This ray heads toward F, emerging parallel to the principal axis after reflection. Ray 3: This ray travels toward the center of curvature C; as a result, the ray strikes the mirror perpendicularly and reflects back on itself. |
| Mirror Equation |
1/do + 1/di = 1/f
di is negative for an image behind the mirror, as it for a virtual image. |
| Magnification Equation | m = - di/do |
| Sign Conventions | |
| Object Distance |
do is +
if the object is in front of the mirror(real object)
do is - if the object is behind the mirror (virtual object) |
| Image Distance |
di is +
if the object is in front of the mirror(real image)
di is - if the object is behind the mirror (virtual image) |
| Focal length |
f is + for a concave mirror
f is - for a convex mirror |
| Magnification |
m is + for an image that is upright with respect to the object
m is - for an image that is inverted with respect to the object |
| Refraction | The change in direction as light passes from one medium into another is called refraction. |
| The index of refraction |
The index of refraction (or refractive index) n
is the ratioof the speed of light c in a vacuum tothe speed of light
v on the material:
|
| An apparent depth |
Because of refraction, a submerged object has an apparent depth
that is different than its actual depth and for the observer who is directly
above the object, the apparent depth d' is
related to the actual depth d:
|
| Total internal reflection | If all the incident light is reflected back into the medium from which it came, a phenomenon called total internel reflection. |
| Dispersion | The spreading of light into its color components is called dispersion. |
| Converging lenses | With a converging lens paraxial rays that are parallel to the principal axis are focused to a focal point on the axis by the lens and its dostance from the lens is the focal length f. |
| Diverging lenses | With a diverging lens paraxial rays that are parallel to the principal axis are appear to originate from the focal point F after passing through the lens. |
| Ray Diagrams | |
| Converging Lens |
Ray 1.
This ray initialy travels parallel to the principal axis.
In passing through a converging lens,
the ray is refracted toward the axis
and travels through the focal point
on the right side of the lens.
Ray 2. This ray first passes through the focal point on the left and then is refracted by the lens in such a way that it leaves traveling parallel to the axis. Ray 3. This ray travels directly through the center of the lens without any appereciable bending. |
| Diverging Lens |
Ray 1.
This ray initially travels parallel to the principal axis.
In passing through a diverging lens, the ray is refracted
away from the axis, and appears to have originated from
the focal point on the left of the lens.
Ray 2. This ray leaves the object and moves toward the local point on the right of the lens. Before reaching the focal point, however, the ray is refracted by the lens so as to exit parallel to the axis. Ray 3. This ray travels directly through the center of the thin lens without any appreciable bending. |
| The human eye | |
| A retina | In the human eye, a real, inverted image is formed on a light-sensitive surfase, called retina. |
| An accommodation | Accommodation is the process by which the focal lenth of the eye is automatically adjusted, so that objects at different distances produce focused images on the retina. |
| The near point | The near point of the eye is the point nearest the eye at which an object can be placed and still produce a sharp image on the retina. |
| The far point | The far point of the eye is the location of the farthest object on which the fully relaxed eye can focus. |
| A nearsighted eye | A nearsighted (myoptic) eye is one that can focus on nearby objects, but not on distant ones. It can be corrected by wearing eyeglasses or contacts made from diverging lenses. |
| A farsighted eye | A farsighted (hyperoptic) eye can see distant objects clearly, but not those close up. Farsightedness can be corrected by using converging lenses. |
| The refractive power of a lens |
The refractive power of a lens is measured in diopters
and is given by 1/f, where f is the focal length
of the lens in meters.
A converging lens has a positive refractive power. A diverging lense has a negative refractive power. |
| Magnification Equation |
Image height / Object height =
|
| Sign Conventions | |
| Object Distance |
do is +
if the object is to the left of the lens (real object),
as is usually the case.
do is - if the object is to the right of the lens (virtual object). |
| Image Distance |
di is + for an image
(real) formed to the right of the lens by a
real object.
di is - for an image (virtual) formed to the left of the lens by a real object. |
| Focal length |
f is + for a converging lens.
f is - for a diverging lens. |
| Magnification |
m is + for an image that is upright with respect to the object.
m is - for an image that is inverted with respect to the object. |
| A magnifying glass | A magnifying glass is usually a single converging lens that forms an enlarged, upright, and virtual image of an object placed at or inside the focal point of the lens. |
| A compound microscope | A compound microscope usually consists of two lenses, an objective and an eyepiece. The final image is enlarged, inverted, and virtual. |
| An astronomical telescope | An astronomical telescope magnifies distant objects with the aid of an objective and eyepiece, and it produces a final image that is inverted and virtual. |
| Spherical aberration | Spherical aberration occurs because rays that pass through the outer edge of a lens with spherical surfaces are not focused at the same point as those that pass through the center of the lens. |
| Chromatic aberration | Chromatic aberration arises because a lens focuses different colors at different points. |
Unit 14