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d o = d i .

An extended object such as the container in [link] 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.

Multiple images

If an object is situated in front of two mirrors, you may see images in both mirrors. In addition, the image in the first mirror may act as an object for the second mirror, so the second mirror may form an image of the image. If the mirrors are placed parallel to each other and the object is placed at a point other than the midpoint between them, then this process of image-of-an-image continues without end, as you may have noticed when standing in a hallway with mirrors on each side. This is shown in [link] , which shows three images produced by the blue object. Notice that each reflection reverses front and back, just like pulling a right-hand glove inside out produces a left-hand glove (this is why a reflection of your right hand is a left hand). Thus, the fronts and backs of images 1 and 2 are both inverted with respect to the object, and the front and back of image 3 is inverted with respect to image 2, which is the object for image 3.

Figure shows cross sections of two mirrors placed parallel to each other, mirror 1 being on the left and mirror 2 on the right. Four human faces are shown, labeled object, image 1, image 2 and image 3. The object is in between the two mirrors, facing left towards mirror 1. Image 1 is to the left of mirror 1, facing right. Image 2 is to the right of mirror 2, facing right. Image 3 is to the far left, facing left. It is smaller than the other three faces.
Two parallel mirrors can produce, in theory, an infinite number of images of an object placed off center between the mirrors. Three of these images are shown here. The front and back of each image is inverted with respect to its object. Note that the colors are only to identify the images. For normal mirrors, the color of an image is essentially the same as that of its object.

You may have noticed that image 3 is smaller than the object, whereas images 1 and 2 are the same size as the object. The ratio of the image height with respect to the object height is called magnification    . More will be said about magnification in the next section.

Infinite reflections may terminate. For instance, two mirrors at right angles form three images, as shown in part (a) of [link] . Images 1 and 2 result from rays that reflect from only a single mirror, but image 1,2 is formed by rays that reflect from both mirrors. This is shown in the ray-tracing diagram in part (b) of [link] . To find image 1,2, you have to look behind the corner of the two mirrors.

Figure a shows mirror 1 and mirror 2 placed at right angles to each other and a lego man in front of them. Mirror 1 shows image 1, mirror 2 shows image 2 and the image of image 1, labeled image 1,2. Figure b shows cross section of two mirrors at right angles to each other. Mirror 1 is placed horizontally at the top and mirror 2, vertically, to the right. The object is a human face, upright and facing right, towards mirror 2. Image 1 is above mirror 1, upside down and facing right. Image 2 is to the right of mirror 2, upright and facing left. Image 1,2 is at the top right corner, upside down and facing left.
Two mirrors can produce multiple images. (a) Three images of a plastic head are visible in the two mirrors at a right angle. (b) A single object reflecting from two mirrors at a right angle can produce three images, as shown by the green, purple, and red images.

Summary

  • A plane mirror always forms a virtual image (behind the mirror).
  • The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.

Conceptual questions

What are the differences between real and virtual images? How can you tell (by looking) whether an image formed by a single lens or mirror is real or virtual?

Virtual image cannot be projected on a screen. You cannot distinguish a real image from a virtual image simply by judging from the image perceived with your eye.

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Can you see a virtual image? Explain your response.

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Can you photograph a virtual image?

Yes, you can photograph a virtual image. For example, if you photograph your reflection from a plane mirror, you get a photograph of a virtual image. The camera focuses the light that enters its lens to form an image; whether the source of the light is a real object or a reflection from mirror (i.e., a virtual image) does not matter.

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Can you project a virtual image onto a screen?

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Is it necessary to project a real image onto a screen to see it?

No, you can see the real image the same way you can see the virtual image. The retina of your eye effectively serves as a screen.

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Devise an arrangement of mirrors allowing you to see the back of your head. What is the minimum number of mirrors needed for this task?

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If you wish to see your entire body in a flat mirror (from head to toe), how tall should the mirror be? Does its size depend upon your distance away from the mirror? Provide a sketch.

The mirror should be half your size and its top edge should be at the level of your eyes. The size does not depend on your distance from the mirror.

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Problems

Consider a pair of flat mirrors that are positioned so that they form an angle of 120 ° . An object is placed on the bisector between the mirrors. Construct a ray diagram as in [link] to show how many images are formed.

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Consider a pair of flat mirrors that are positioned so that they form an angle of 60 ° . An object is placed on the bisector between the mirrors. Construct a ray diagram as in [link] to show how many images are formed.

Figure shows cross sections of two mirrors placed at an angle of 60 degrees to each other. Six small circles labeled object, I1, I2, I3, I4 and I5 are shown. The object is on the bisector between the mirrors. Line 1 intersects mirror 1 perpendicularly connecting the object to I1 on the other side of the mirror. Line 2 intersects the mirror 2 perpendicularly connecting the object to I2 on the other side of the mirror. Lines parallel to these respectively connect I2 to I3 and I1 to I4. Lines parallel to these respectively connect I4 to I5 and I3 to I5.

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By using more than one flat mirror, construct a ray diagram showing how to create an inverted image.

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Practice Key Terms 6

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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