The following are some problems of convex lens imaging law.

In optics, an image gathered by actual light, called a real image, can be accepted by the light curtain; On the contrary, it is called a virtual image, which can only be felt with the eyes. When talking about the difference between real images and virtual images, we often mention such a method of distinction: "The real images are all upside down, and the virtual images are all upright." The three virtual images formed by plane mirror, convex lens and concave lens are all positive; The real image formed by concave lens and convex lens, and the real image formed by pinhole imaging are all inverted without exception. Of course, concave lenses and convex lenses can also form real images, and the two real images they form are also inverted.

When the distance between the object and the lens is greater than 1 times the focal length, the object becomes an inverted image. This is like the convergence point of actual light, which can be accepted by the light curtain and is a real image. When the distance between the object and the lens is less than 1 focal length, the object becomes an upright virtual image. When the object is infinitely far away, the obtained image is infinitely close to 1 times the focal length, but it is always farther than 1 times the focal length.

If it is a thick meniscus concave lens, the situation will be more complicated. When the thickness is large enough, it will be equivalent to a galileo telescope, and when the thickness is larger, it will be equivalent to a positive lens.

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The difference between convex lens and concave lens

Different structures

The convex lens is composed of transparent mirror surfaces polished into spherical surfaces on both sides, and the edge of the convex lens is thin and the middle is thick.

A concave lens is composed of a transparent mirror body, both sides of which are polished into concave spherical surfaces, and the concave lens has a thick edge and a thin middle.

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Have different effects on light.

A convex lens mainly focuses light.

Concave lenses mainly diverge light.

Different imaging characteristics

The convex lens is refractive imaging, and the image can be upright or inverted; Virtual image and real image; Zoom in and out. Play the role of spotlight.

Concave lens is refractive imaging, which can only be reduced to vertical virtual image. Play the role of astigmatism.

Lens and mirror

Lenses (including convex lenses) are instruments that transmit light and form images by folding the light. Light obeys the law of refraction.

Mirror (including convex mirror) is an instrument that does not transmit light, but reflects back the image, and light obeys the law of reflection.

The convex lens can be an inverted enlarged, equal-sized and reduced real image, or an upright enlarged virtual image. Parallel light can converge on the focal point, and the light emitted from the focal point can also be refracted into parallel light. Concave mirror can only become an upright and reduced virtual image, which is mainly used to broaden one's horizons.

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Detailed imaging law

Convex lens imaging rule table

Object distance (u) and

The relationship between focal length (f) and image distance (v)

The relationship of object distance (u) applies the relationship between the inverted size of the same side or different sides of the feature and virtual reality.

U=∞ (infinity)-The opposite profile becomes a very small bright spot. The focal length of a convex lens is measured by sunlight (the distance between the sun and the earth is close to infinity)—

U & gt2fu & gtv inverted miniature real-world camera-

U = 2fu = v is used to measure the cut-off point of the focal length of a real image (such as an inverted image).

F<u & lt2fv & lt Inverted Magnifying Real Image Projector

Slide projector-

U = FV =∞ Non-imaging —— Real-Virtual Boundary Point of Focal Length Measurement of Parallel Light Source

U & ltfv & ltu vertical magnifying virtual image magnifying glass on the same side. The virtual image is on the same side of the object, and the virtual image is behind the object.

Text abstract

( 1)

When the object is located beyond twice the focal length of the convex lens, it becomes an inverted reduced real image; When the object is located at twice the focal length of the convex lens, it becomes a real image with inverted size;

When the object is located between one focal length and two focal lengths of the convex lens, it becomes an inverted magnified real image; When the object is located at the focal length of the convex lens, it does not image;

When an object is located within a focal length of a convex lens, it becomes an upright magnified virtual image; When the object is infinitely far away, the image becomes a very small and bright point, and it is still a real image.

When forming a real image, the object image is on different sides of the convex lens; When a virtual image is formed, the object and the image are on the same side of the convex lens.

(2)

Double focal length divides reality into reality.

Double focal length and fractional size

The near-focus image of the object becomes larger.

The far-focus image becomes smaller.

Note: the focal length refers to the distance from the point where the parallel light source converges on the main optical axis through the lens to the optical center of the lens, which can also be directly called the focal length; Twice the focal length means twice the distance.

Two demarcation points of convex lens imaging;

2f point is the dividing point of real image enlargement and reduction; Point f is the dividing point between real image and virtual image.

Lens imaging satisfies the lens imaging formula:

1/u (object distance)+1/v (image distance) = 1/f (lens focal length)

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Convex lens imaging experiment

optical bench

In order to study various conjectures, people often experiment with optical bench.

(1) During the experiment, it is necessary to adjust the heights of the convex lens and the light screen to keep their centers on the same horizontal line with the center of the candle flame, so as to ensure that the image of the candle flame can be formed in the center of the light screen.

(2) During the experiment, keep the position of the convex lens unchanged, change the distance between the candle or light screen and the convex lens, and observe and record the experimental phenomena.

According to the experiment, the lens imaging optical path is made.

(1) Put the candle away from the focal length of 2 times and observe the phenomenon.

② Place the candle between 2 times focal length and 1 times focal length, and observe the phenomenon.

(3) Put the candle in a focal length and observe the phenomenon.

④ Optical path of convex lens imaging.

The experimental study on the imaging law of convex lens is as follows: when the object distance is within a focal length, an upright and enlarged virtual image is obtained; When the focal length is between 1-2 times, the inverted magnified real image is obtained; Beyond the double focal length, the real image is reversed and reduced.

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Examples and applications of convex lens imaging

human eye

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 must be a real image. According to the above rule of thumb, the image of the object on the retina seems to be upside down. But anything we usually see is obviously upright. This problem, which conflicts with experience and law, actually involves the regulation of cerebral cortex and the influence of life experience.

When the distance between the object and the convex lens is greater than the focal length of the lens, the object becomes an inverted image. When an object approaches the lens from a distance, the image becomes larger and the distance from the image to the lens becomes larger. When the distance between the object and the lens is less than the focal length, the object becomes an enlarged image. This image is not the convergence point of the actual refracted light, but the intersection point of their opposite extension lines, which can not be received by the light screen and is a virtual image. The contrast of the virtual image formed by the flat mirror (which can't be received by the light screen, but can only be seen by the eyes).

camera

The lens of a camera is a convex lens, the scene to be photographed is an object, and the film is a screen. The light irradiated on the object is diffusely reflected by the convex lens and imaged on the final film; When the film is coated with photosensitive substances, chemical changes will occur after exposure, and the image of the object will be recorded on the film.

The relationship between object distance and image distance is exactly the same as the imaging law of convex lens. When the object approaches, the image gets farther and bigger, and finally becomes a virtual image on the same side. The object distance increases, the image distance decreases and the image becomes smaller; The object distance decreases, the image distance increases and the image becomes larger. One focal length is divided into virtual reality and the other is divided into size.

other

Projectors, slide projectors, projectors, magnifying glasses, searchlights, cameras and video cameras all use convex lenses, which improve our lives and are used all the time. Hyperopia glasses are convex lenses and myopia glasses are concave lenses.

In addition, the convex lens is also used for:

1, shooting, video recording

2. Projections, slides and movies

3, used for special lighting (focusing on various colors)

4. Virtual images are used to enlarge people, artifacts and maps.

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Method of legal deduction

The imaging rule of convex lens is1/u+1/v =1/f (that is, the sum of the reciprocal of object distance and image distance is equal to the reciprocal of focal length. ) * * * There are two kinds of derivation methods. They are "geometric method" and "functional method"

Geometric method

The title is shown in the right picture, and it is proved by geometric method that1/u+1/v =1/f.

Derivation of convex lens imaging law by geometric method

Solution: △ABO∽△A'B'O

∴AB:A'B'=u:v

∫△COF∽△A ' b ' f

∴CO:A'B'=f:(v-f)

∵ quadrilateral ABOC is a rectangle.

∴AB=CO

∴AB:A'B'=f:(v-f)

∴u:v=f:(v-f)

∴u(v-f)=vf

∴uv-uf=vf

∫uvf≠0

∴(uv/uvf)-(uf/uvf)=vf/uvf

∴ 1/f- 1/v= 1/u

Namely:1/u+1/v =1/f.

structuralfunctionalism

The problem is as shown on the right. Prove1/u+1/v =1/f by function method.

Solve the foundation

The right picture shows the schematic diagram of convex lens imaging.

Where c is the length of the imaged object and d is the length of the image formed by the object. U is the object distance, v is the image distance, and f is the focal length.

step

(1) In order to solve this problem by the function method, the main optical axis of the convex lens is related to the horizontal coordinate axis (X axis) of the plane rectangular coordinate system, the ideal refractive surface of the convex lens is related to the vertical coordinate axis (Y axis), and the optical center of the convex lens is related to the coordinate origin. Then: the coordinates of point A are (-u, c), point F is (f, 0), point A' is (v, -d), and point C is (0, c).

(2) AA' and A'C extend in two directions into a straight line l 1, l2, which are regarded as two function images. As can be seen from the image, the straight line l 1 is a direct ratio function image, and the straight line l2 is a linear function image.

(3) Let the analytical formula of the straight line l 1 be y=k 1x, and the analytical formula of the straight line l2 be y = k2x+b..

According to the meaning of the question, substitute a (-u, c), a' (v, -d) and c (0, c) into the corresponding analytical equation:

c=-u k 1

-d=k2v+b

c=b

Let k 1 and k2 be the unknown solution:

k 1=-(c/u)k2=-(c/f)

∴ Two resolution functions:

y=-(c/u)x y=-(c/f)x+c

∴ The coordinate (x, y) of the intersection point a' of two functions conforms to the equation.

y=-(c/u)x

y=-(c/f)x+c

∫A '(v，-d)

∴ replaced:

-d=-(c/u)v

-d=-(c/f)v+c

∴-(c/u)v=-(c/f)v-c=-d

∴(c/u)v=(c/f)v-c=d

cv/u=(cv/f)-c

fcv=ucv-ucf

fv=uv-uf

∫uvf≠0

∴fv/uvf=(uv/uvf)-(uf/uvf)

∴ 1/u= 1/f- 1/v

Namely:1/u+1/v =1/f.

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Conventional memory

1.[ 1]?

1 . u & gt； 2f, reverse and reduce the real image f < v & lt2f camera.

The abbreviation is: the outside is small and solid (or the distant image of the object becomes smaller)

2.u=2f and inverted image v=2f can be used to measure the focal length of convex lens.

The abbreviation is: Pairs are equal to reality (or objects are equal to images that remain unchanged).

3.2f & gtu> Inverted Enlarged Real Image v & gt2f Projector, Slide projector, projector

Referred to as: Chinese and foreign things are big (or things are close and things are far away)

4.u=f non-imaging parallel light source: searchlight.

Abbreviation: points do not image (or objects do not image with the same focal length)

5.u<f magnifies the virtual image vertically, and there is no virtual image on the same side of the object magnifying glass.

Abbreviation: the point is full of empty space (or the small focal length of an object looks like a big empty space)

Note: If u is greater than 2f, it is simply called farther from the convex lens. U is less than 2f and greater than f, which means near is closer to the convex lens.

Second,

Three images of things, two small objects, two images, and three large objects and images are on the same side.

The close-up image of the object becomes larger and the close-up image of the object becomes smaller. 1 times focal length is divided into virtual reality, and 2 times focal length is divided into size.

Third,

I found a small camera outside the Second Ring Road.

Between the first and second sounds, I saw a huge projection.

The first ring, play 3 fake 4 serious 5.

Note: ① Outside the second ring: outside the double focal length.

2 pick up: pick up, real (real image. Inverted (inverted) application: camera

③ Punching: Enlarge.

(4) False and virtual (virtual image)

⑤ Warp and magnifying glass

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Examples of convex lens applications

Example 1 Grandma often does this when she reads the newspaper with a magnifying glass, in order to see a bigger and clearer picture ().

A. Keep the newspaper and magnifying glass still and keep your eyes off the newspaper.

B. Keep your eyes still and keep the magnifying glass away from the newspaper.

C keep the newspaper and magnifying glass still and keep your eyes close to the newspaper.

D. Keep your eyes still and put the magnifying glass close to the newspaper.

Analysis: Magnifier is a convex lens. It can be seen from the convex lens imaging experiment that when the object is in a focal length, the greater the object distance, the greater the image distance and the larger the image. It can also be concluded from the imaging principle that the light parallel to the principal axis is constant, but as the object moves away from the lens, the light passing through the optical center becomes more and more gentle, so the farther the intersection of the opposite extension lines of two rays is from the lens, the larger the image is. That is, when the focal length is less than 1 times, the closer the object is to the focal length, the larger the image is. So the answer is B.

Example 2 Xiaoming holds an experimental magnifying glass with a relatively large diameter and stretches out his arms to look at distant objects. He can see images of objects. The following statement is correct ().

A. the light entering the eyes must be emitted by the image.

B. the image must be a virtual image.

C.the elephant must be upside down

D. the image must be enlarged

Analysis: Magnifier is a convex lens. When you hold the convex lens in your hand and straighten your arms to see distant objects, the object distance is much larger than twice the focal length, so it will be imaged on the inside of your hand slightly larger than twice the focal length. The human eye is at arm's length, so the light entering the human eye must be refracted light that is converged and imaged and then separated. We see it as if it were emitted from an image. This image must be the true image of inverted restoration. So the answer is C. In option A, not all the light that enters the human eye comes from the image.

Second, as the application of projector lens.

Example 3 When screening a movie in the countryside and testing the lens, I found that the image on the screen was a little small. How should I adjust the projector ()?

A. The projector is farther away from the screen and the film is farther away from the lens.

B. The projector is farther away from the screen and the film is closer to the lens.

C The projector is closer to the screen and the film is farther away from the lens.

D. The projector is closer to the screen and the film is closer to the lens.

Analysis: This is an application problem of convex lens. The focal length of the lens (convex lens) of a film projector is constant. According to the imaging law of convex lens, the closer the film is to the focus of the lens, the larger the image formed on the screen and the farther the screen is from the lens.

In convex lens imaging, the closer the object is to the focus, the bigger the image is and the farther it is from the convex lens (both real and virtual images have this law). On the contrary, the farther the object is from the convex lens, the smaller the real image is and the closer the image is to the focus. In concave lens imaging, the farther the object is from the concave lens, the smaller the image and the closer the image is to the virtual focus.

As can be seen from the above analysis, the correct option for this question is B.

Thirdly, it is used as a camera lens.

Example 4 A classmate wants to take a single photo after taking a picture of graduation photo. The method that a photographer should take is ()

A. Bring the camera closer to your classmate, and at the same time, retract the camera and bring the film closer.

B. Keep the camera close to your classmates, and at the same time, extend the camera forward, away from the film.

C Keep the camera away from classmates, and at the same time retract the lens and get close to the film.

D Keep the lens away from classmates, and at the same time, the lens extends forward and away from the film.

Analysis: The camera lens is equivalent to a convex lens. Behind the lens is a black box, and the film is installed at the bottom of the black box, which is equivalent to a light screen; Take a single photo after taking a group photo. It seems to be getting bigger. When imaging, we should enlarge the image, narrow the object distance and increase the image distance, that is, lengthen the black box or extend the lens forward. As can be seen from the above analysis, the correct option for this question is B.

Example 5 When shooting objects at the bottom of the pool with a camera, if the position of the camera remains the same, there is water and there is no water in the pool (assuming that the objects seen by human eyes are the same size in both cases), then there is water ().

A. The camera box should be shorter and the image should be larger.

B. the camera box should be shorter and the image will be smaller.

C. The camera box should be slightly longer, and the image will be slightly larger.

D. The black box should be longer and the image should be smaller.

Analysis: According to the principle of camera imaging, when the object distance decreases, the image distance increases. In order to get a clear image of the object on the film, the black box should be lengthened appropriately, and at the same time, the image on the film will be slightly larger than the original image.

In this example, with and without water, the distance between the object at the bottom of the pool and the camera lens is different; Due to the refraction of light, when there is water in the pool, the object distance decreases. According to the imaging principle, the correct option is C.

When surveying and mapping, surveyors need to take pictures of the ground on the plane in the air, which is called aerial photography. If the focal length of the lens of an aerial camera is 50mm, the distance from the negative to the lens is ().

A.10mm away

B. slightly less than 50 mm

C. slightly more than 50 mm

D. equal to 50 mm