Magnification Method .
The Purpose of Experiment : Determine the Focal Length of a Convex Lens .
The Apparatus : Convex lens , illuminated object , image screen and optical
The Theory ( Introduction ) :
There are two types of lenses : the convergent ones (convex lens) and the divergent ones (concave lens). The convergent ones are more important. A converging lens can be used in two ways : as an image producer and as a magnifier.
The first way; image producer, mans that the convex lens with a focal length f can produce a " real image". An image is said to be real because when rays from a given point on the object pass through a lens and converge at a respective point on the other side of the lens. As in the figure below :
From the geometry of the figure above, there is a simple relationship between u, v and f ; it is
1/f = 1/u + 1/v …………….(1)
Where u is the distance between object and lens
v is the distance between image and lens
f is the focal length of the lens
Also, the convex lens can be used as a magnifier. When looking through a convex lens, an image that is often larger or smaller than the actual object is seen. The ratio of image height to object height is called "magnification". It is notable that magnification M may be larger or smaller than 1. The magnification M can be expressed as following :
M = h/h° = v / u ………….(2)
And from equations (1) and (2)
v/f = v/u + 1 v/u = v/f − 1 M = v/f – 1 ……….(3)
The Method :
1. Put the lens at a certain distance from the illuminated object.
2. Move the image screen along the optical bench until a sharply defined image of the object is formed on the screen.
3. Measure the height image h, object distance u, and image distance v.
4. Gradually increase the distance of the object from the lens and take further sets of reading.
5. Calculate the Value of magnification for each set, using equation 2.
6. Plot a graph with values of M as ordinate against corresponding values of v as abscissa.
7. Find the focal length from the slope; slope = 1/f.
The Discussion :
A ray of light passing through a glass lens maybe refracted twice- first where it enters the glass and, then where it leaves the glass. There is a net deviation of the ray from its original direction. Usually each surface of the lens is part of a sphere.
Lenses with two spherical surfaces sufficiently close together that the distance between them ( the thickness of a lens) can be neglected are called thin lenses . If their thickness cannot be neglected, they are called thick lenses.
The focal length of an optical system is a measure of how strongly it converges (focuses) or diverges (defocuses) light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus. A system with a shorter focal length has greater optical power than one with a long focal length; that is, it bends the rays more strongly, bringing them to a focus in a shorter distance.
In telescopy and most photography, longer focal length or lower optical power is associated with larger magnification of distant objects, and a narrower angle of view. Conversely, shorter focal length or higher optical power is associated with a wider angle of view. In microscopy, on the other hand, a short objective lens focal length leads to higher magnification.
For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative, and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.
For an optical system in air, the effective focal length gives the distance from the front and rear principal planes to the corresponding focal points. If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium. Some authors call this distance the front (rear) focal length, distinguishing it from the front (rear) focal distance, defined above.
The relationship between u, v and f when m = 1 :
Since M = v / u and M =1 v = u
Since M = v / f – 1 and M = 1 1 + 1 = v / f 2 = v/f v = 2f
v = u = 2f when m = 1
1. Human eye represents a convex lens with 2 cm in focal length. The image appears small and inverted on the light sensitive retina at the eyeball, but the brain automatically corrects for this.
2. The convex lens can be used as a magnifying glass which is a simple converging lens with short focal length that can make an object image on the retina larger.
3. Another important application of the convex lens is the compound microscope, which contains two convex lens with certain geometry. The magnification in this instrument is higher than that by magnifying glass.
The References :
1. [ندعوك للتسجيل في المنتدى أو التعريف بنفسك لمعاينة هذا الرابط]
2. [ندعوك للتسجيل في المنتدى أو التعريف بنفسك لمعاينة هذا الرابط]
عدل سابقا من قبل دكتوره في السبت فبراير 27, 2010 10:52 pm عدل 1 مرات