Distorted Images in Curved Mirrors
Summary
Introduction
Have you ever visited a house of mirrors and seen a wacky-looking version of yourself? In this activity you can construct your own miniature house of mirrors. Try it out and see what funny reflections you can make!
Materials
- Mirror paper, available from a craft, paper supply store, or available online from Amazon. New, unwrinkled aluminum foil can be used, but the images will be fuzzier, and the observations will not be as clear.
- Old flip-flop that can be damaged. If unavailable, use an old insole or thick cardboard.
- Two skewers
- Small, colorful objects. Figurines are fun, but the cap of a pen, a battery, an eraser, etc. work just as well. If you use aluminum foil instead of mirror paper, it is important to choose brightly-colored objects.
- Stainless steel spoon; as new as possible, without nicks or dents
- Optional: Glue
- Optional: Stainless steel cups, pots, ladles, etc.
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Prep Work
- To make a bendable mirror, cut a rectangle of your mirror paper to cover the sole of the flip-flop (or other backing you will use).
- Lay the flip-flop on the table in landscape orientation (so that the long side is parallel to the side of the table).
- Turn it over so the sole side faces up.
- Place the rectangle of mirror paper on top with the mirroring side facing up.
- Carefully stick one skewer through the mirror paper into the flip-flop an inch or so from the right edge, and stick the second skewer a few centimeters from the left edge of the flip-flop. The skewers should stick straight up from the flip-flop.
- If needed, use glue to keep the skewers in place.
Instructions
- Turn your mirror on its side so the long side rests on the table, mirrored side facing you. Place a small object on the table in front of the mirror. If your object is skinny and tall, lay it on its side. Can you see the reflection in the mirror?
- Compare the reflection of the object in the mirror to the object.
Do they look identical? Are the size and color the same? Do they appear to stand at the same location? - Push the sides of the mirror back so the middle bulges out toward you. This type of curved mirror is called a convex mirror.
Compare the reflection of the object in the convex mirror to the object. Do they look identical? If not, how do they look different?
- Let the mirror go back to being flat, and then push the middle backward and the sides forward so the middle of the mirror caves in. This type of curved mirror is called a concave mirror.
Compare the reflection of the object in the concave mirror to the object. Do they look identical? If not, how do they look different?
- Repeat the previous three steps with a few other objects.
Do you observe similar things each time? When do objects elongate or become shorter? In what direction do they change?
- The skewers stick straight out from the mirror. Scientists call this line the normal to the surface.
Do you see that for a flat mirror they are parallel to each other?
- Look what the skewers do when you create a convex mirror.
Are they still parallel to each other? If not, do the tips of the skewers get closer to each other or spread out more?
- Create a concave mirror and look again.
Are the skewers parallel to each other? If not, do the tips of the skewers get closer to each other or spread out more?
- Incident and reflected light rays always make a perfectly symmetrical V shape with the normal as a line of symmetry. For a flat mirror the normals (represented by the skewers) are parallel. For a concave or convex mirror, the normals point inward and outward, respectively. This is similar to what is happening with the reflected light rays: they come together when the mirror bends inward (concave) and move apart when the mirror bulges out (convex).
Can you use this knowledge to explain the distortions seen in the reflections in a concave and convex mirror? This is a hard question. Do not despair if you do not find it!
- Have some fun with your mirror. Take the mirror in your hands, hold it in landscape orientation in front of you so you see your face in the flat mirror.
How do you think your face will look if you curve the mirror one way, and then the other way?
- Bend the mirror to make it a convex mirror.
How does your face look in a convex mirror? Was your prediction correct?
- Bend the mirror to make it a concave mirror.
How does your face look in a concave mirror? Was your prediction correct?
- If you can, bend your mirror so the shiny surface has a wavy form.
What does the reflection of your face look like now?
- Turn the mirror in portrait orientation (so it is tall and narrow) and explore some more. Bend it one way and then the other.
Do you see a pattern in your observations? Does a concave mirror always distort the image in the same way? What about the convex mirror?
- The mirror you just used curved along one direction. Now you will explore a reflection in a mirror that is curved in all directions, like a spoon.
What do you think your reflection on the outside of the metal spoon will look like? What do you think will happen when you mirror yourself in the inside of the spoon?
- Try mirroring yourself in the outside of a metal spoon, and then in the inside. (The newer the spoon, the clearer the image will be.) Repeat with a small object.
What do you observe? Was your prediction correct?
- Take a small object and move it away from and then closer to the inside of the spoon. Now bring it very close, until it is almost touching.
Is the reflection still upside-down when you have the object close? Why do you think this happens?
What Happened?
Did you see distorted reflections in the curved mirrors? Light rays that shine off a point on an object travel in all directions. Those reaching the mirror bounce back like a ball would bounce on a smooth surface. Some will travel into the eye. The location where these reflected light rays or their extensions meet is where the brain thinks the object is, so that is where the object appears to be when you see it in the mirror.
For the flat mirror, the skewers, which represent the normal to the surface, are parallel to each other. This creates reflected rays that meet at a point behind the mirror so the image appears at the other side of the mirror. For a flat mirror, the reflection is the same size and appears at the same distance from the mirror as the actual object.
For a convex mirror the skewers pointed outward. In this case light rays bounce the same way with respect to the normal but because the skewers point away from each other, the rays seem to spread out more compared to the ones reflecting on a flat mirror. These rays also meet at a point behind the mirror, but not as far behind it as the flat mirror. An object reflected in a convex mirror appears closer to the mirror and smaller than it really is.
For a concave mirror the skewers point toward each other, and the reflected light rays spread out less. The reflection of an object close to the mirror is bigger and looks farther away. If the skewers were long enough, they would have met at a point before the mirror. Move the object closer to the point where the skewers meet, and the reflected rays will spread out less. As a result the object will seem bigger and farther away. The reflection gets so big that your mirror probably only covers a fraction of it. Once you cross the point where the skewers meet, something strange happens: you see the object inverted! The right and left sides (if your mirror is in landscape orientation) or top and bottom (if you hold the mirror in portrait orientation) of the image are switched! This happens because the light rays meet before the mirror, so a light ray that starts at the right or the top will reflect back toward the left or the bottom. The inside of the spoon is curved in the horizontal and vertical direction, so right and left sides and top and bottom of the image are switched.
Digging Deeper
We see an object when light reflected from the object shines into our eyes. From that input of light, the brain uses the eyes' signals to reconstruct a picture of the object.
The brain makes a few assumptions in this process of reconstructing a picture. One assumption is that the light rays traveled in a straight line from the object to the eye. Although a light ray usually travels in a straight line, in some cases it can change direction first—for example, when a light ray enters or leaves a transparent material, such as water, or bounces off a shiny material, such as a mirror. Your brain still runs the usual reconstruction process, treating the image as if it were created by rays that traveled in a straight line. As a result, your brain might reconstruct a picture that looks different than the original object; your brain might have been fooled!
Light reflecting off of a surface is kind of like a ball bouncing on a floor. If the floor is flat and you drop the ball straight down, the ball will hit the floor and reverse direction, bouncing straight up. This direction is called the normal to the surface. If you drop the ball at an angle to this normal, it will bounce back at the other side of the normal, but with the same angle to the normal. The same principle applies to light reflecting (or bouncing back) from a surface. In this case, the ray of light approaching the surface is known as the incident ray. If the incident ray strikes the reflective surface at a particular angle, the reflected ray leaves the surface at the same angle—but is located at the other side of the normal. In other words, the incident and reflected ray make a perfectly symmetrical V shape, with the normal as the line of symmetry.
Mirrors reflect almost all of the light hitting their surface. In addition, they have a very smooth surface and are usually flat, causing light to reflect in an orderly way, reflecting a good but "mirror image" of objects. This results in a neat image on the retina and thus a clearly reconstructed picture. Shiny surfaces that are not perfectly smooth can lead to blurry or fuzzy pictures.
Mirrors make it possible to see a picture of yourself or of objects that are behind you. As you observed in this activity, they do not always give an accurate representation of how you or the objects behind you look. Mirrors can fool you!
Ask an Expert
For Further Exploration
- Take your homemade mirror and bend it into a concave shape. Bend it quite far and estimate the point where the skewers would touch if they were long enough. Maybe your skewers do touch! Place an object closer to the mirror than that point, and one farther away. Adjust your position and the position of the objects so you can see the reflection of the objects in the mirror. Can you see what is strange about the reflection of the object farther away? Can this help you find out when the reflection in a concave mirror is reversed, and when it is not?
- Take small objects and see what their reflections look like in shiny stainless steel cups, pots, ladles, etc. Can you understand what you see?
Related Resources
Project Ideas
Activities
Lesson Plans
- MS-PS4-2. Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials.
Links
- Scientific American: Can You Create an Infinite Number of Reflections?
- Scientific American: Sight-Line Science: Candle in the Mirror
- Concave Mirror - Why is your reflection upside down on a spoon?, from It's Aumsum Time
- Why is a convex mirror used as a rear view mirror?, from It's Aumsum Time
- The Reflection of Light, from Optics 4 Kids
