Sunday, April 19, 2009

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to reflect light rays and focus them on a point and with the help of a secondary mirror to deflect the real image is formed outside.



PROBLEM
Increase image.
An Object of 4 cm. high is placed 15 cm. a concave spherical mirror. If the image formed is located at 22.5 cm of this, How tall is this?

Saturday, April 18, 2009

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concave spherical mirrors Convex Mirrors: Concave and Convex


a situation occurs in which the image is virtual, upright and smaller than the object











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:

concave mirrors:


1. Object at the left of center of curvature. The image is real, inverted and located between the center and focus. Its size is smaller than the object.
2. Object at the center of curvature. The image is real, inverted and placed in the same spot. Its the same size as the object.
3. Object located between the center of curvature and focus. The image is real, inverted and located on the left of center of curvature. It is larger than the object.
4. Object at the focus of the mirror. The reflected rays are parallel and the image is formed at infinity.
5. Right object at the focus. The image is virtual, and maintains its orientation. It is larger than the object.



a) Subject to the left of the center of curvature. The image is real, inverted and located between the center and focus. Its size is smaller than the object.

b) Property located in the center of curvature. The image is real, inverted and placed in the same spot. Its size As the object.

c) Property located between the center of curvature and focus. The image is real, inverted and located on the left of center of curvature. It is larger than the object.

d) object at the focus of the mirror. The reflected rays are parallel and the image is formed at infinity.

e) Subject to the right of the outbreak. The image is virtual, and maintains its orientation. It is larger than the object. There

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called equipupilar minimal increase, calculated by dividing by 6 the diameter of the objective expressed in mm.
If we use a longer focal length eyepiece that gives this increase, the beam of parallel rays emerges from the eye for every star observed exceed the diameter of the iris and lose some of the light, which enter the target without entering the eye.
The conditions are very different with a telescope in orbit, as has recently been launched into space. There is no atmosphere to disturb and increased is limited only by the wave nature of light.

image of a star much increased, given by a perfect telescope without atmospheric disturbance.

linear value depends on the wavelength of light and lens focal ratio.
L.22 l F r = 1.22 lf / D
This linear value of r as seen from the center of the lens defines a very small angle is
r = 1.22 l / D (radians)

Example:
Be a telescope with a lens diameter D = 300 mm. It is known that the wavelength of light to the center of the visible spectrum is l = 0.56 m or mm (microns or micrometers: drive is a millionth of a meter, or 10-6 m 0.000001 mm .) As we express this quantity in mm. we have:


l = 0.00056 mm (1 m = 1000 mm)
We will then:


r = 1.22 x 0.00056 / 300 = 2.2773 x10-6 radians = 0.4697 "

To move to
arcsec multiply radians per 206265, ie the number of seconds of arc are in a radian.


And if the telescope is 1500 mm example. focal length, the linear value of r is
rf r = 3.416 m.



This means that the telescopes will be difficult to separate two points on objects at an angular distance equal to r.

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image magnification imaging spherical mirrors

A spherical mirror is characterized by its radius of curvature R. In the case of spherical mirrors there is only one focal point F = F '= R / 2 whose position coincides with the midpoint between the center of the mirror and the vertex thereof. Will be on the left of the vertex to the concave mirrors and convex mirrors right.

Increased mirror will be A = y '/ y depends on the curvature of the mirror and the position of the object.

The construction of images is very easily done using the main beams:


• Parallel Ray: Ray optical axis parallel to the upper part of the object. Refracted after passing through the image focus. • Lightning focal
: Ray from the top of the object and passes through the focal object, which is refracted in a way that goes parallel. Refracted after passing through the image focus.
• Radial Ray: Ray from the top of the object and is directed toward the center of curvature of the diopter. This beam is not refracted and continues in the same direction as the angle of incidence is zero.


MAIN ELEMENTS OF SPHERICAL MIRRORS

1) Center of curvature (C): In a spherical mirror is the center of the sphere it belongs to the optical surface


2) Radio curvature (R): In a mirror is the radius of the sphere.

3) Optical axis: the line is determined by the center of the disk mirror, called vertices (V) and its Center of Curvature (C)



4) Main Focus (F): The point at which converge the rays reflected by the mirror, when it impinges on a beam parallel to its optical axis
. The main focus located on the optical axis, equidistant from V and ofC.




5) Aperture: The opening line is the diameter (D) of the mirror. The opening angu1ar (a) is the angle with vertex at the focus F whose sides pass through the ends of a diameter.
6) Focal Length (f): The distance between the vertex V of the mirror and its focus F. Turns out to be f = R / 2.
7) focal ratio (f): the ratio between focal length f and diameter D of the mirror: F = f / D.
8). Focal Plane: The plane perpendicular to the optical axis passing through the principal focus F.
9) Arrow (j): It is the small segment between the vertex and the midpoint of an optical diameter of the mirror.


Tuesday, April 14, 2009

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Mirror is the name given to any surface or laminated glass silvered by the later, or brushed metal, so that it reflected objects. By extension is called mirror to any surface that produces reflection of objects, eg. : Water surface.


Elements of spherical mirrors:

curvature Center: The center of the field to cap belongs.

bending radius: The radius of the sphere it belongs to the mirror.

Vertex Mirror: The pole of the spherical cap to which the mirror.

Main Shaft: The line through the apex and the center of curvature

Secondary axis: Each of the lines passing through the center of curvature.

opening (or angle) of the mirror: The angle formed by the secondary axes passing through the edge of the mirror.

In the spherical mirrors are checked the same laws of reflection in plane mirrors. In fact, it is considered that the point of incidence of the beam belongs to the plane tangent to the spherical mirror, at that point.


The path of the rays and outbreaks:

In concave spherical mirrors, it holds that:

All the major axis parallel rays are reflected through the focus (located on the main shaft).


• Any beam passing through the principal focus is reflected parallel to the main shaft.


• Every ray that passes through the center of curvature, are reflected on himself. This is easily explained in geometric form, as if passing through the center of curvature, is a radio and all radio is perpendicular to the tangent to the circle at the point where this radius intersects the circumference.


• It can be shown geometrically that the main focus of a spherical mirror is the midpoint of the radius of curvature. Given the relationship between this and the focal length, we can also say-and prove-that the focal length is equal to half the radius of curvature.

far we have spoken of concave spherical mirrors, let us turn now to the convex :

These also comply with the law of reflection known and analyzed, but we must make the clarification that: the main focus of a spherical convex mirror is virtual, therefore, the focal length of a convex mirror is negative.



can easily verify that the path of the rays in the cases of convex spherical mirrors, is similar to the path in the concave mirrors, but ... as the focus is virtual, we say:

• Any beam parallel to the main axis in a convex mirror is reflected so that its extension passes through the focus.


• Each ray incident on a convex mirror tends to go through the focus is reflected parallel to the main shaft.


• Any incident beam toward the center of the mirror, it reflects on itself.

The picture that emerges in a spherical convex mirror is virtual, in the same direction and less than the object reflected.