## Friday, January 13, 2012

### Why things are not as they appear to be?

You are likely familiar with this sign on the side-view mirrors of some cars: "Objects in the mirror are closer than they appear."

There are so many signs and instructions in the car that you probably avoid wondering about them up until your kids with their natural curiosity ask you: WHY? Let's try to run ahead of this question and figure out this WHY?
Why and how do you think these side-view mirrors distort reality?

Your thoughts and ideas accepted any time until midnight on Sunday Janury 15th(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Kim said...

The side view mirror is convex (curves outward) because a flat mirror in that position would not provide the range of visibility required for a driver looking from the side trying to look behind them. The curved mirror provides a "wide angle" which pulls more of the rear into the image. But by pulling more in, it needs to compress the image, and that means that what you're seeing is smaller than it would otherwise be. Since it's smaller, our brain interprets that as farther away. Hence the warning "objects in the mirror are closer than they appear" which is important to remember, particularly if it's a dinosaur coming at you! (I loved that scene in Jurassic Park).

anne-marie said...

The mirror we see in the picture is the right or passenger's mirror. This mirror surface is convex in order for the driver to see more. This mirror display more objects to avoid the blind spot but the objects appear less big than they are and then they also appear farther( more depht). I believe that the left one has a flat surface( at least it will make sense).

Jerome said...

There are two types of mirrors on an automobile.

1. A flat mirror on the driver's left side (in places like Canada and the United States) and the interior middle of the vehicle.

2. A convex mirror on the right side.

The right mirror is convex because
a. It helps to reduce the size of the blind spot.
b. It helps see using the right side. The driver has a narrower field of vision if a flat mirror were used.

Regulations require that both types of mirrors be mounted on a car no matter the make if sold in Canada and the US.

Tom said...

It's a convex mirror (it bulges out slightly). The glass might be flat, or it might not, but the mirrored surface is convex.

The "math" is easier to draw (geometry) than to explain verbally, for me anyway. Light (image) from an increased wide field is reflected by this convex mirror into an image at your eye, and that new image is a good deal smaller than would be delivered by a flat mirror.

It's clearer if one draws the light-path in reverse, from the viewer's eye to various points on the bulging mirror's face, reflected out to the objects in the world.

And so all the objects (trees, cars, bicycles, pedestrians) are made to seem smaller, and farther away, than they really are. Conversely, they actually are closer than they appear.

Ilya said...

This would be a good time to draw some pictures, but I will try with words given the medium we've got! The side view mirrors are not flat, but convex. If they were flat, they would not cover wide enough field of view that is required by their function. Here is a way to prove it: drawing the reflection paths from the driver to the left and right extremes of a flat side-view mirror will quickly demonstrate that the driver would get only a narrow window of that side of the road no matter how the mirror is oriented. By making the mirror convex, we increase the field of view. Intuitively, wider field of view in the same amount of "screen space" has to mean that the objects are seen as smaller compared to a "flat mirror" that shows less. But again this can be proven more strictly by drawing reflection paths in the convex and flat mirror cases, demonstrating that the same physical size (e.g. width of a car you would see through a side view mirror) will result in smaller projection on the convex mirror. The human eye not being used to this, will interpret these smaller projections same way as though these objects are being looked at via a flat mirror. Knowing the relative size of an object being looked at (e.g. a passenger car), the human brain estimates the distance accordingly (to be larger than it really is). Thus the need for the warning.

Jerome said...

I just wondered about something I may have said. I sort of have a right, left, east, west dyslexia, not a good thing for a math teacher.

The right mirror (the one that makes things smaller and further away) is meant to reduce the "blind area" closer to the car than a flat mirror.

A flat mirror more or less shows the correct size and correct distance but you really see less of the area behind you.

The right mirror is a convex mirror.

What I'm really doing is checking to see that I've said left and right correctly.

Here are some of the properties of a convex mirror.

http://en.wikipedia.org/wiki/Curved_mirror

The article states that the image is never turned upside down (though it is smaller), it is virtual (the rays don't do what our eyes tell us they do) and objects appear to be further away.

I consider some of the stuff I came across to be quite controversial. Like this one. Sorry, I'll always shoulder check the lane I want to go into.

Annie said...

The passenger side mirror is convex allowing for a wider field of view. Without getting into the physics of it, convex mirror images are smaller and therefore appear further away than they really are. This might lead a driver to make a dangerous lane change while assuming that the car is further away than it is.

Maria said...

A lot of fascinating details and great explanations.
- Not all mirrors in a car are made the same.
- Right side mirror or both side mirrors on some cars are convex, bulging out like a Christmas bauble and compressing a large view into a smaller space.
- Objects on such mirrors appear smaller than they actually are and our brain interprets them to be further away than they actually are.
- Kim reminded us that there is a scene in Jurassic park that features a dinosaur in a side view mirror.
- Jerome posted a very interesting link on how to adjust your mirrors to get rid of any blindspots in your car. I am going to try it today but wondering whether this depends on a size of a car.

Anonymous said...

fold all of the baubles because they are paper and when Christmas comes again open them!