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

[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.

Homework Equations

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

 

[phinds]

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??

Homework Equations

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.

EDIT: Oh. Perhaps that's your point. You KNOW your math is wrong and are asking why?

 

[Suyash Singh]

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.

EDIT: Oh. Perhaps that's your point. You KNOW your math is wrong and are asking why?

No my math is correct.

 

[kuruman]

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.

 

[kuruman]

"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.