Convex lens is based onRefraction of lightIt is made by principle.Convex lens is a lens with thick center and thin edge.Convex lenses can be divided into biconvex, flat convex, concave convex (or crescent shaped) and other forms. Convex lenses have the function of converging light lines, so they are also called convergent lenses. Thick convex lenses have the function of telescope and convergence, which is related to the thickness of the lens.Long sight glasses are convex lenses.[1]
Convex lens has amplification effect.Convex lens twicefocal lengthAccording to size, one time of focus is divided into real and virtual.
Convex lens
takeparallellight(such as sunlight) shines into the convex lens parallel to the main optical axis (the line connecting the spherical centers of the two spheres of the convex lens is called the main optical axis of the lens)Two passes on both sides of the lensrefractionThen, focus on a point on the axis, which is called the focal point of the convex lens (marked F, English: focal point). The convex lens has a real focal point on both sides of the mirror. If it is a thin lens, the distance between the two focal points and the lens center is approximately equal.The focal length of a convex lens is the distance from the focal point to the center of the lens, usually expressed as f.The smaller the spherical radius of convex lens is, the focal length (mark:f, in English: focal length).Convex lens can be used for magnifying glass, presbyopia and glasses, camera, film projector, slide projector, microscope, telescopelens(lens), etc.Main optical axis: the straight line passing through the two spherical centers C1.C2 of the convex lens is called convex lensMain optical axis。Optical center: The central O point of convex lens is lensOptical center。 Focus: the light parallel to the main axis will converge at a point F on the main optical axis after passing through the convex lens, which is a convex lensfocus。 Focal length: the distance from focus F to convex lens optical center O is calledfocal length, usingfexpress.Object distance: distance scale from object to optical center of convex lensObject distance, usinguexpress.Image distance: distance scale from the image formed by the object through the convex lens to the optical center of the convex lensImage distance, usingvexpress.
In fact, convex lens and concave lens do not have a certain focus. Only the rays parallel to the main optical axis and equidistant from the main optical axis will completely intersect on the main optical axis.The reason why we see that many rays passing through the convex lens parallel to the main optical axis but with unequal distance to the main optical axis have a "focus" is that the curvature radius of the convex lens surface is large, and the difference of light deflection degree is not obvious.For the convenience of use, we take the intersection point of two rays whose distance from the main optical axis is equal to the distance from the top of the convex lens as the focus of the convex lens.
The formula can be deformed to get f=uv/(u+v) or u=vf/(v-f) or v=uf/(u-f)
When light passes through a convex lens, it is refracted once only in the middle (here at the y-axis).(Although there are too many letters, there are only a few useful ones at last) Note: x (red) axis - convex lens main optical axis y (blue) axis - convex lens O - optical center F - focus f - focal distance u - object distance v - image distance a - object length purple line - light passing through optical center orange line - parallel light green line - parallel light passing through focus green lineThe straight line analytical formula of purple line is obtained: green line, y=- (a/f) x+a;Purple line, y=- (a/u) x The next step is to calculate the coordinates of two intersections (in fact, it is only necessary to calculate the abscissa v) y=- (a/f) x+a=- (a/u) x x/f-1=x/u ux uf=fx where x is v uv uf=fvuv=vf+uf divided by v+u f=uv/(u+f)
Convex lens imaging
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Imaging principle
The object is placed outside the focus and becomes an inverted real image on the other side of the convex lens. The real image can be reduced, equal sized, or enlarged.The smaller the object distance, the larger the image distance, and the larger the real image.The object is placed in the focus and forms an upright magnified virtual image on the same side of the convex lens.The larger the object distance, the larger the image distance, and the larger the virtual image.No imaging when in focus.It will become a real image of isometric handstand when it is at twice the focal length.
In optics, the image gathered by the actual light is called the real image, which can be undertaken by the light screen;On the contrary, it is called virtual image, which can only be felt by the eyes.Experienced physics teachers, when telling the difference between real images and virtual images, often mention such a distinction method: "Real images are inverted, while virtual images are upright." The so-called "upright" and "inverted", of course, are relative to the original object.
The three virtual images formed by plane mirror, convex mirror and concave lens are upright;The real image formed by concave mirror and convex lens, as well as the real image formed by pinhole imaging, are all inverted without exception.Of course, concave mirrors and convex lenses can also form virtual images, and the two virtual images they form are also upright.
Convex lens imaging
So is the image formed by human eyes a real image or a virtual image?We know that the structure of the human eye is equivalent to a convex lens, so the image of external objects on the retina is a theorem.Presbyopia, that is, the light passing through the lens in front of the eyeball is not fully assembled, like falling behind the retina.As a convex lens, the presbyopia is corrected by first gathering the light to make the image fall on the retina.When the distance between the object and the lens is greater than the focal length, the object becomes an inverted image. This image is formed by the light emitted by the candle to the convex lens converging through the convex lens. It is the convergence point of the actual light, which can be carried on by the light screen. It is a real image.When the distance between the object and the lens is less than the focal length, the object becomes an upright virtual image.
(1)
Beyond the double focal length, reduce the real image by handstand;Double focus equal size;
One to two focal lengths, upside down to enlarge the real image;One time focal length does not image;
Enlarge the virtual image vertically within one focal length;
The real image and image are on the opposite side of the convex lens, and the virtual image is on the same side of the convex lens.
(2)
One time focal length is divided into virtual and real, and two times focal length is divided into size.
Imaging rule
Convex lens imaging law
Object to convex lens
Distance u (object distance)
Image to convex lens
Distance v (image distance)
Like
size
Like
Up-down
Like
Falsehood and sthenia
application
example
u>2f
2f>v>f
narrow
handstand
Real image
camera
u=2f
v=2f
Isometric
handstand
Real image
Focal length
2f>u>f
v>2f
enlarge
handstand
Real image
Projector projector
u=f
None (parallel v infinity)
nothing
nothing
nothing
searchlight
u<f
nothing
enlarge
Orthostatic
Virtual image
magnifier
When u<f, the image and object are on the same side of the lens
Imaging optical path method
Optical path diagram of convex lens and concave lens imaging
(1) The object is beyond the focus of 2 times
(2) The object is between 2 times focal length and 1 time focal length
(3) The object is in focus
(4) Concave lens imaging optical path
Measuring focal length
1. Formula method: use the optical tool holder to do the experiment of convex lens forming real image, measure and record the object distance u and image distance v during imaging, calculate the lens focal length f according to the lens imaging formula, and take the average value after multiple measurements.
2. Conjugation method: fix the position of the light source and light screen with the light fixture base, and measure their spacing L.Place the convex lens of the focal length to be measured between them, and move the convex lens along the main axis, so that the light screen displays the inverted image of the light source twice.Record the position of the lens during the two imaging, and then calculate the distance d of the lens movement during the two imaging. According to the formula, the convex lens focal length f can be calculated, which is called the conjugate method.This is one of the common methods for measuring the focal length of convex lens in the laboratory.
3. Parallel light focusing method: according to the characteristics of the convex lens, let the parallel light (such as sunlight) incident on the convex lens along the main axis direction, place a light screen parallel to the lens on the other side, adjust the position of the light screen so that the light spot on the light screen is the smallest and brightest. At this time, the distance between the lens and the light screen is the focus of the convex lens.This is a simple method for measuring the focal length of convex lens roughly.
4. Far object imaging method: In the laboratory, the far object imaging method can also be used to estimate the focus of convex lens instead of the parallel light focusing method, which is similar to the parallel light method;Adjust the position of the light screen so that distant objects (such as the windows of the classroom or objects outside the window) are imaged on the light screen. The distance between the light screen and the lens is approximately the focal length of the lens.
experimental study
The imaging law of convex lens is: when the object distance is within one time of the focal length, the upright and magnified virtual image is obtained;The inverted and enlarged real image is obtained when the focal length is between one and two times;When beyond the double focal length, the inverted and reduced real image is obtained.
The purpose of this experiment is to study and confirm this rule.In the experiment, there is the following table:
Optical path diagram of convex lens imaging under different conditions
Imaging law of convex lens
Object distance u
Upright or upside down
Zoom in or out
Virtual image or real image
Same side and different side with the object
Image distance v
u>2f
handstand
narrow
Real image
Opposite side
f<v<2f
u=2f
handstand
Isometric
Real image
Opposite side
v=2f
f<u<2f
handstand
enlarge
Real image
Opposite side
v>2f
u=f
No imaging, because v=infinity (parallel, so infinity)
u<f
Orthostatic
enlarge
Virtual image
Ipsilateral
f<v<2f
This is the table designed to prove that rule.In fact, lens imaging meets the lens imaging formula:
The camera uses the imaging law of convex lens.The lens is a convex lens, the object to be photographed is the object, and the film is the screen.The light shining on the object passes through diffuse reflection and convex lens to form the image of the object on the final film. The film is coated with a layer of light sensitive material, which changes chemically after exposure, and the image of the object is recorded on the film.The relationship between object distance and image distance is exactly the same as that of convex lens.When the object is near, the image becomes farther and farther, larger and larger, and finally becomes a virtual image on the same side.
In addition, when the object is at infinity, the image can be approximately considered to be at the focus.(Because of this, the point and shoot camera does not need to focus) When the object is far away from the convex lens, the image will be close to the convex lens, that is to say, in which direction the object goes, the image will go.When an object moves from infinity to a distance image 2F, the object moves faster than the image.
Formula derivation
As shown in the figure, the light emitted by the object AB that is parallel to the main optical axis crosses the focal point F2 and the light passing through the lens center crosses the point E
Then DE is the real image, BO is the object distance u, and DO is the image distance v
This is a positive solution
From similar triangles, we can get BO/OD=AB/DE
CO/DE=OF2/F2D
From the rectangular ABOC, we can get AB=CO
thereforeOF2/F2D= AB/DE=BO/OD
That is, f/(v-f)=u/v
Uv uf=vf (cross multiplication)
uv=uf+vf
Uv/f=u+v (divide both sides by f at the same time)
V/f=1+v/u (divide both sides by u)
1/f=1/u+1/v (divide both sides by v)
difference
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Differentiation method
1. Touch method (thin middle edge is concave lens, thin middle edge is convex lens)
3. Magnification method (put the lens on the word, and the word after viewing is magnified is convex lens, and reduced is concave lens)
4. Shake method (place the lens on the word and move it to one side. The direction of the word is the same as that of the lens, which is concave lens, and the opposite is convex lens)
Different from concave mirror
1、 Different structures
Difference between convex lens and concave lens
The convex lens is composed of a transparent mirror body whose two sides are ground into spherical surfaces;
Concave mirror is composed of a mirror body with one side concave and the other side opaque
2、 Different imaging properties
Convex lens is refraction imaging, and the image can be: positive, inverted;Virtual and real;Zoom in and out.Convex lens is used to collect light.
Difference between convex lens and concave lens
Concave mirror is a real image that can be reduced or enlarged upside down in reflection imaging, and can also be a virtual image that can be magnified vertically.The astigmatic lens (including convex lens) is an instrument that allows light to pass through and image after light refraction. Light obeys the law of refraction.The surface mirror (including convex mirror) is not an instrument that allows light to pass through, but reflects back to image. Light obeys the law of reflection.The convex lens can be a real image with inverted magnification, equal size and reduction, or a virtual image with upright magnification.The parallel light can be focused on the focus, and the light emitted by the focus can also be refracted into the parallel light.Concave mirrorIt can only form an upright magnified virtual image, mainly with divergent light.
Difference from concave lens
1、 Different effects on light
Convex lens mainly concentrates light
Concave lens mainly diverges light
2、 Different imaging
Convex lens can form a large real image such as upright magnified virtual image, inverted magnified real image, inverted reduced real image;
A concave lens can only form an upright reduced virtual image.
3、 Different focus
Convex lens has real focus and 2 focuses
Concave lens has virtual focus
4、 Different uses
Convex lens for hyperopia glasses
Concave lens for myopia glasses
matters needing attention
1. When using convex lens, do not touch the lens by hand.
2. When there is strong sunlight, do not point the convex lens at the flammable and explosive articles, otherwise the explosive articles will be ignited and cause explosion.
Magnification of convex lens
The magnification of a convex lens (virtual image, positive image) is only related to the focal length of the lens, and the virtual image and object are on the same side of the lens.
The calculation formula is: photopic distance (25CM)/focal length=magnification.
The shorter the focal length, the higher the magnification.
The imaging multiple (real image, inverted image) of convex lens is related to the image distance, and the real image and object are on both sides of the lens.
Its imaging formula: 1/focal length=1/object distance+1/image distance
The closer the object is to the focus, the larger the image distance and the larger the image.The magnification of the real image is not limited by the focal length of the lens.
The surface of a convex lens is an arc, which is part of a circle. The radius of the arc can be measured. This radius is called the radius of curvature of the lens arc.It is obvious that the smaller the radius of curvature, the higher the central convex of the lens, the greater the thickness of the lens, and the shorter the focal length of the lens.
