Plane Mirrors: Virtual Images
A familiar virtual image: a reflection in a mirror
Our reflection in a mirror is a familiar example of a virtual image. The image is called virtual because the light does not really come from the position of the image. Two rays of light are traced in the diagram: at each reflection, angle of incidence equals angle of reflection. From simple geometry, we see that the image is the same size as the object . So the magnification is +1, where the ‘+’ indicates that it is right way up. If the object were in a plane at the same distance from the mirror, we could observe that the line AB is half the length of ab. So, to see yourself in the mirror from head to toe, you need a mirror that is half as tall as you are.
In the photo, you’ll notice that my image appears to be smaller than me. In fact, the image is the same size, but it looks smaller because it is further away from the camera. I am about half a metre from the mirror, and, in the geometry used for this photo, the mirror and I are both the same distance from the camera. But the image is half a metre behind the mirror, so it is half a metre more distant from the camera than I am.
Real And Virtual Images
The images formed by a lens can be:
- upright or inverted
- magnified or diminished
- real or virtual
is an image that can be projected onto a screen. A virtual image appears to come from behind the lens.
To draw a ray diagram:
Some ray diagrams may also show a third ray.
What Is An Image Of An Object
The image of an object is the location where light rays from that object intersect upon reflecting from a mirror. There are two types of image: real and virtual image.
More precisely, when a beam of rays from a point source suffers a change in direction due to refection or refraction and the refracted or reflected rays converge or appear to diverge from another point, then the second point is known as an image.
Two types of images are formed based on whether the beam of rays converge or diverge at a given point real image and virtual image.
A real image and a virtual image are different forms of image. The main difference between real and virtual images lies in the way in which they are produced. A real image is formed when rays converge, whereas a virtual image occurs where rays only appear to diverge.
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Selected Solutions To Problems & Exercises
1. 4.00 1600
3. 0.501 cm Eyepiece should be 204 cm behind the objective lens.
5. +18.3 cm 60.0 11.3 cm +6.67 400
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Example 4 Image Produced By A Concave Lens
Suppose an object such as a book page is held 7.50 cm from a concave lens of focal length 10.0 cm. Such a lens could be used in eyeglasses to correct pronounced nearsightedness. What magnification is produced?
Strategy and Concept
This example is identical to the preceding one, except that the focal length is negative for a concave or diverging lens. The method of solution is thus the same, but the results are different in important ways.
To find the magnification m, we must first find the image distance di using thin lens equation \frac}=\frac-\frac}}\\, or its alternative rearrangement }=\frac}}}-f}\\.
We are given that f = 10.0 cm and do = 7.50 cm. Entering these yields a value for \frac}}\\:
This must be inverted to find di:
Now the magnification equation can be used to find the magnification m, since both di and do are known. Entering their values gives
|Table 1. Three Types of Images Formed By Thin Lenses|
|negative||positive m< 1|
In Image Formation by Mirrors, we shall see that mirrors can form exactly the same types of images as lenses.
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What Is The Power Of Lens
The power of a lens can be defined as the measure of the degree of convergence or divergence of the light rays falling on it. The degree of divergence or convergence depends upon the focal length of the lens. Thus, the power of the lens can be defined as the reciprocal of the focal length of the lens used. It is given as,
Where f is equal to the focal length of the lens used. SI unit of power is Dioptre . The power of the concave lens is said to be negative, while the power of the convex lens can be positive.
Oblique Parallel Rays And Focal Plane
We have seen that rays parallel to the optical axis are directed to the focal point of a converging lens. In the case of a diverging lens, they come out in a direction such that they appear to be coming from the focal point on the opposite side of the lens . What happens to parallel rays that are not parallel to the optical axis )? In the case of a converging lens, these rays do not converge at the focal point. Instead, they come together on another point in the plane called the focal plane. The focal plane contains the focal point and is perpendicular to the optical axis. As shown in the figure, parallel rays focus where the ray through the center of the lens crosses the focal plane.
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Why Does A Mirror Seem To Invert Left To Right But Not Top To Bottom
|My image seems to off his/my left hand to shake||In this photo, the mirror really does invert left to right|
As above, let’s call the normal direction from the mirror the x axis. As we saw in the diagram above, the image in the mirror is inverted in the x axis. In the photo at right, the mirror really does invert left to right: my extended right hand is closest to the mirror while the reflection’s extended hand is also closest to the mirror. In the photo at left, the image is also inverted in the x direction, so here it is inverted front to back. Why do we look at this reflection and think that it is inverted left to right?
The answer is that I am approximately symmetrical: my left side is very much like my right. So, when we look at my front-to-back reflection in the photo at left, we could imagine that it is just me, but rotated 180° about a vertical axis. Except for one thing: my imagined rotation would have to put down the right hand and extend the left. For that reason, we imagine the front-to-back inverted reflection as a 180° rotation plus a left-to-right inversion. Finally, we should note that a mirror can invert top to bottom: all I’d have to do is to lie on the floor with my feet towards the mirror!
Focussing With A Concave Mirror
|A nearly spherical mirror focusses the sun’s light on a small area of paper and ignites it.|
If this mirror were perfectly parabolic and if it were pointed directly at the sun, then it would focus the radiation onto a very small region near the focal point.
The mirror is not parabolic: a good parabolic mirror of this size would be used for an extremely good amateur telescope or a research instrument such as a patrol telescope. We obtained this one cheaply for demonstrations and, for that purpose the aberration it produces is actually useful!
This mirror is approximately but not very accurately spherical. We can see in this movie that the shape of the bright image is not even symmetric, so the mirror is not symmetric. Nevertheless, by minimising the size of the image formed by the parallel rays of light from the sun, we get a good measure of the focal length.
The ignition of the paper is also interesting. The solar intensity or energy flux is about 1300 W.m2, so the mirror is concentrating a few hundred watts onto the image area. After just seven seconds, the paper ignites. It follows that a mirror like this is quite dangerous, especially on a sunny day: even focussed on skin it could quickly cause pain, and directed towards the eye it could be blinding.
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Image Formation By Lenses
- List the rules for ray tracking for thin lenses.
- Illustrate the formation of images using the technique of ray tracking.
- Determine power of a lens given the focal length.
Lenses are found in a huge array of optical instruments, ranging from a simple magnifying glass to the eye to a cameras zoom lens. In this section, we will use the law of refraction to explore the properties of lenses and how they form images.
Figure 1. Rays of light entering a converging lens parallel to its axis converge at its focal point F. The distance from the center of the lens to the focal point is the lenss focal length f. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.
Real Images In A Concave Mirror
|An incandescent lamp is the object. Its image is projected on a screen via a concave mirror.|
Here the light really does fall on the screen to form the image, which is therefore a real image. The object and the image are equidistant from the mirror, and this distance is twice the focal length. It is inverted. More about that below.
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Rules For Ray Tracing
What Is Lens Formula
Convex lenses can also be known as converging lenses since the rays converge after falling on the convex lens while the concave lens is known as diverging lenses as the rays diverge after falling on the concave lens. Images formed by these convex lenses can be real or virtual depending on their position from the lens and can have a different size too. The image distance can be calculated with the knowledge of object distance and focal length with the help of the lens formula.
In optics, the relationship between the distance of an object , the distance of an image , and the focal length of the lens are given by the formula which is known as the Lens formula. Lens formula is applicable for concave as well as convex lenses. These lenses have negligible thickness. Lens equation or lens formula is an equation that relates the focal length, image distance, and object distance for a spherical mirror. It is given as,
Lens Formula – 1/u + 1/v = 1/f
v = Distance of the image from the lens.
u = Distance of the object from the lens.
f = Focal length of the lens.
The Mirror Equation: Object Image And Focal Distances
In the next photo, the object is at a distance greater than two focal lengths . The image now lies between f and 2f.
Let’s use the geometry of the ray diagrams sketched above to derive an equation relating the object distance p, the image distance q and the focal length f.
Apologies readers, I still have a diagram to make up here.
Virtual Image And Real Image
An image may be defined as that point, where the light rays coming from an object meet or appears to meet after reflection or refraction.
In this definition the word object may be defined as anything which gives out light rays. The objects can be of two types: very small objects and large objects or extended objects. The small objects are represented by a dot in a ray diagram, while the large objects can be represented by an arrow pointing in upward direction.
Types of Images
The images are of two types:
1. Real images 2. Virtual images
A real image is that image which is formed when the light rays coming from an object actually meet each other after reflection or refraction. A real image can be obtained on the screen. The real image is always inverted. The common example of real image is the image formed on the cinema screen.
A virtual image is that image which is formed when the light rays coming from an object do not actually meet, but appear to meet when produced backwards. These images cannot be obtained on the screen. The virtual image is always erect. The common example of virtual image is the image formed in the mirror when we stand in front of that mirror.
Differences between Real Images and Virtual Images
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Image Formation By Thin Lenses
In some circumstances, a lens forms an obvious image, such as when a movie projector casts an image onto a screen. In other cases, the image is less obvious. Where, for example, is the image formed by eyeglasses? We will use ray tracing for thin lenses to illustrate how they form images, and we will develop equations to describe the image formation quantitatively.
Figure 7. Ray tracing is used to locate the image formed by a lens. Rays originating from the same point on the object are tracedthe three chosen rays each follow one of the rules for ray tracing, so that their paths are easy to determine. The image is located at the point where the rays cross. In this case, a real imageone that can be projected on a screenis formed.
The image formed in Figure 7 is a real image, meaning that it can be projected. That is, light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye, for example. Figure 8 shows how such an image would be projected onto film by a camera lens. This Figure also shows how a real image is projected onto the retina by the lens of an eye. Note that the image is there whether it is projected onto a screen or not.
Locating An Image In A Plane Mirror
The law of reflection tells us that the angle of incidence is the same as the angle of reflection. Applying this to triangles PAB and QAB in and using basic geometry shows that they are congruent triangles. This means that the distance PB from the object to the mirror is the same as the distance BQ from the mirror to the image. The object distance is the distance from the mirror to the object . Similarly, the image distance is the distance from the mirror to the image . If we measure distances from the mirror, then the object and image are in opposite directions, so for a plane mirror, the object and image distances should have the opposite signs:
An extended object such as the container in can be treated as a collection of points, and we can apply the method above to locate the image of each point on the extended object, thus forming the extended image.
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Plane Mirrors And Reflection
A mirror is a reflective surface that does not allow the passage of light and instead bounces it off, thus producing an image. The most common mirrors are flat and called plane mirrors. These mirrors are made by putting a thin layer of silver nitrate or aluminium behind a flat piece of glass.
When you place an object in front of a mirror, you see an image of the same object in the mirror. The object is the source of the incident rays, and the image is formed by the reflected rays. An image formed by reflection may be real or virtual. A real image occurs when light rays actually intersect at the image, and become inverted, or turned upside down. A virtual image occurs when light rays do not actually meet at the image. Instead, you see the image because your eye projects light rays backward. You are fooled into seeing an image! A virtual image is right side up .
In flat, or plane mirrors, the image is a virtual image, and is the same distance behind the mirror as the object is in front of the mirror. The image is also the same size as the object. These images are also parity inverted, which means they have a left-right inversion.
How Hot Can We Make An Image Using A Large Concave Mirror
Another puzzle from the multimedia tutorial: Suppose that we had a perfectly parabolic mirror. Ray optics tells us that, if perfectly parabolic, it would focus light on a point. The larger the mirror, the more of the sun’s radiation it would focus on that very small area: in fact about 1400 watts per square metre of mirror, if we neglect clouds and scattering in the atmosphere. So, with a very small, largely insulated target, larger mirror areas would give more and more power. What is the maximum temperature we could reach?
Thermodynamics tells us that there must be a limit: The temperature of the surface of the sun is about 6000 K. It were possible to heat the target to a higher temperature than that, then we could run a heat engine from the target to the sun: a perpetuum mobile of the second kind: it would violate the second law of thermodynamics. So there must be a catch.
And there is. In later chapters, we’ll analyse diffraction, which depends on the the wavelength of the radiation that produces it. And we’ll also show how the temperature of an object is related to the wavelengths of radiation it emits .
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