# Why Do Objects in Convex Car Mirrors Appear Closer Than They Are?

• Suyash Singh
But with one plane and one convex mirror, the driver's brain is given conflicting information and that's why the warning is needed (assuming that the driver is going to use the convex mirror).In summary, the statement on convex rearview mirrors in cars in India that reads "objects in mirror are closer than they appear" is referring to how the driver's brain interprets the visual message from the eye, not to the mathematically derived distance of the image from the mirror. This is because the comparison of angular separations between the images in the plane and the convex mirror can fool the brain into believing that the object is farther away than it actually is. This warning is necessary because the driver's brain is given conflicting information from the two
Suyash Singh

## Homework Statement

I have noticed that in cars in India on rearview mirror(convex) it is written that "objects in mirror are closer than they appear".
But for convex mirror of focal length 1 metre and object distance 39 metre, the image distance is 39/40 metre .
Which tells that image is closer but object is farther which is contradictory.

1/v+1/u=1/f

## The Attempt at a Solution

v=u/u-f
=u/u-1
for u=-39m,f=1m
v=39/40m

Last edited by a moderator:
Suyash Singh said:

## Homework Statement

I have noticed that in cars in India on rearview mirror(convex) it is written that "objects in mirror are closer than they appear".
But for convex mirror of focal length 1 metre and object distance 39 metre, the image distance is 39/40 metre .
Object is farther than it appears??

1/v+1/u=1/f

## The Attempt at a Solution

v=u/u-f
=u/u-1
for u=-39m,f=1m
v=39/40m
I have not paid attention to your math but if it says that objects in a convex mirror are farther than they appear, then it is clearly wrong.

phinds said:
I have not paid attention to your math but if it says that objects in a convex mirror are farther than they appear, then it is clearly wrong.

No my math is correct.

Most cars have three mirrors, two of them are plane (driver's side and inside overhead) and one is convex (passenger's side). The image of a car behind you is larger in the plane mirror than in the convex mirror. So if you first look in the plane mirror and then in the convex mirror, you might think that the car has fallen farther behind because its image is smaller by comparison when in actuality it has not. In other words, it is "closer" than you might think. At least that's how I understand the meaning of that message and that's why I rarely use the convex mirror when driving.

Suyash Singh
But mathematically the statement comes out to be wrong.

Suyash Singh said:
"objects in mirror are closer than they appear".
The key word is "appear". It refers to how the driver's brain interprets the visual message from the eye, not to the mathematically derived distance of the image from the mirror. Most car driver would not know how to do the calculation and putting the equation on the mirror would be no help either. There is nothing inherent in the virtual image that tells you its distance from the mirror. Additional information is needed.

Stand before a plane mirror with your face 1 m away from it. Take a photo of the mirror. Back off to 2 m and take another photo. Now trim the photos so that the frame of the mirror is not shown and the dimensions of the pictures are the same. Anyone seeing the pictures will say that the distance of your face from the mirror is the same in the pictures. I am reminded of a stanza from the "Hunting of the Snark" by Lewis Carroll,

"He had bought a large map representing the sea,
Without the least vestige of land:
And the crew were much pleased when they found it to be
A map they could all understand."

It is the additional information of the angular separation between points on your face and the frame that let's you judge the distance. As I indicated in my previous post, the comparison of angular separations between the images in the plane and the convex mirror fools your brain into believing that the car behind you is farther than it actually is. It is ingrained in our brains that "the same object looking smaller must be farther away." If all the rear view mirrors in a car were identically convex, the information given by them would be identically interpreted by the driver and no warning would be necessary.

Suyash Singh

## 1. How does a rearview mirror work?

A rearview mirror works by reflecting light from behind the car into the driver's eyes, allowing them to see what is happening behind the car without turning their head. The mirror is angled in a way that it reflects the light from behind, while also allowing the driver to see out the back window.

## 2. Can a rearview mirror be adjusted?

Yes, most rearview mirrors can be adjusted to fit the height and seating position of the driver. This is important for ensuring that the driver has the best possible view out of the back window.

## 3. How do I know if my rearview mirror is properly adjusted?

The rearview mirror should be adjusted so that the driver can see the entire back window without having to move their head. If the mirror is not properly adjusted, the driver may have blind spots and not be able to see all of the cars behind them.

## 4. Do all cars have rearview mirrors?

Yes, all cars are required to have a rearview mirror by law. It is an important safety feature that allows drivers to see behind them and make necessary adjustments while driving.

## 5. Can a rearview mirror be replaced?

Yes, if a rearview mirror is damaged or broken, it can be replaced. However, it is important to have it replaced by a professional to ensure that it is properly installed and adjusted for optimal visibility.

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